diff --git a/dev_tools/qualtran_dev_tools/notebook_specs.py b/dev_tools/qualtran_dev_tools/notebook_specs.py
index 0f9840569..1a2f84e7c 100644
--- a/dev_tools/qualtran_dev_tools/notebook_specs.py
+++ b/dev_tools/qualtran_dev_tools/notebook_specs.py
@@ -104,6 +104,8 @@
import qualtran.bloqs.multiplexers.black_box_select
import qualtran.bloqs.multiplexers.select_base
import qualtran.bloqs.multiplexers.select_pauli_lcu
+import qualtran.bloqs.optimization.k_xor_sat
+import qualtran.bloqs.optimization.k_xor_sat.guided_hamiltonian
import qualtran.bloqs.optimization.k_xor_sat.kikuchi_guiding_state
import qualtran.bloqs.phase_estimation.lp_resource_state
import qualtran.bloqs.phase_estimation.qubitization_qpe
@@ -804,6 +806,21 @@
# ----- Optimization ---------------------------------------------------
# --------------------------------------------------------------------------
OPTIMIZATION: List[NotebookSpecV2] = [
+ # ----- Preliminaries ------------------------------------------
+ NotebookSpecV2(
+ title='Guided (sparse) Hamiltonian Problem',
+ module=qualtran.bloqs.optimization.k_xor_sat.guided_hamiltonian.guided_hamiltonian,
+ bloq_specs=[
+ qualtran.bloqs.optimization.k_xor_sat.guided_hamiltonian.guided_hamiltonian._GUIDED_HAMILTONIAN_DOC,
+ qualtran.bloqs.optimization.k_xor_sat.guided_hamiltonian.guided_hamiltonian._GUIDED_HAMILTONIAN_PHASE_ESTIMATION_DOC,
+ ],
+ ),
+ # ----- Algorithm ------------------------------------------
+ NotebookSpecV2(
+ title='kXOR: Instance load Oracles',
+ module=qualtran.bloqs.optimization.k_xor_sat.load_kxor_instance,
+ bloq_specs=[qualtran.bloqs.optimization.k_xor_sat.load_kxor_instance._LOAD_INSTANCE_DOC],
+ ),
NotebookSpecV2(
title='Planted Noisy kXOR - Kikuchi Guiding State',
module=qualtran.bloqs.optimization.k_xor_sat.kikuchi_guiding_state,
@@ -811,7 +828,35 @@
qualtran.bloqs.optimization.k_xor_sat.kikuchi_guiding_state._SIMPLE_GUIDING_STATE_DOC,
qualtran.bloqs.optimization.k_xor_sat.kikuchi_guiding_state._GUIDING_STATE_DOC,
],
- )
+ ),
+ NotebookSpecV2(
+ title='Planted Noisy kXOR: Kikuchi Adjacency List',
+ module=qualtran.bloqs.optimization.k_xor_sat.kikuchi_adjacency_list,
+ bloq_specs=[
+ qualtran.bloqs.optimization.k_xor_sat.kikuchi_adjacency_list._KIKUCHI_NONZERO_INDEX_DOC
+ ],
+ ),
+ NotebookSpecV2(
+ title='Planted Noisy kXOR: Kikuchi Adjacency Matrix',
+ module=qualtran.bloqs.optimization.k_xor_sat.kikuchi_adjacency_matrix,
+ bloq_specs=[
+ qualtran.bloqs.optimization.k_xor_sat.kikuchi_adjacency_matrix._KIKUCHI_MATRIX_ENTRY_DOC
+ ],
+ ),
+ NotebookSpecV2(
+ title='Planted Noisy kXOR: Block-encoding the Kikuchi Matrix',
+ module=qualtran.bloqs.optimization.k_xor_sat.kikuchi_block_encoding,
+ bloq_specs=[
+ qualtran.bloqs.optimization.k_xor_sat.kikuchi_block_encoding._KIKUCHI_HAMILTONIAN_DOC
+ ],
+ ),
+ NotebookSpecV2(
+ title='Algorithm: Planted Noisy kXOR',
+ module=qualtran.bloqs.optimization.k_xor_sat.planted_noisy_kxor,
+ bloq_specs=[
+ qualtran.bloqs.optimization.k_xor_sat.planted_noisy_kxor._PLANTED_NOISY_KXOR_DOC
+ ],
+ ),
]
# --------------------------------------------------------------------------
diff --git a/docs/bloqs/index.rst b/docs/bloqs/index.rst
index 3f0dbbac0..098b1b5ef 100644
--- a/docs/bloqs/index.rst
+++ b/docs/bloqs/index.rst
@@ -147,7 +147,13 @@ Bloqs Library
:maxdepth: 2
:caption: Optimization:
+ optimization/k_xor_sat/guided_hamiltonian/guided_hamiltonian.ipynb
+ optimization/k_xor_sat/load_kxor_instance.ipynb
optimization/k_xor_sat/kikuchi_guiding_state.ipynb
+ optimization/k_xor_sat/kikuchi_adjacency_list.ipynb
+ optimization/k_xor_sat/kikuchi_adjacency_matrix.ipynb
+ optimization/k_xor_sat/kikuchi_block_encoding.ipynb
+ optimization/k_xor_sat/planted_noisy_kxor.ipynb
.. toctree::
:maxdepth: 2
diff --git a/qualtran/bloqs/optimization/k_xor_sat/__init__.py b/qualtran/bloqs/optimization/k_xor_sat/__init__.py
index 4cbf2722c..a31a1fe90 100644
--- a/qualtran/bloqs/optimization/k_xor_sat/__init__.py
+++ b/qualtran/bloqs/optimization/k_xor_sat/__init__.py
@@ -11,5 +11,9 @@
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
+from .kikuchi_adjacency_list import KikuchiNonZeroIndex
+from .kikuchi_adjacency_matrix import KikuchiMatrixEntry
+from .kikuchi_block_encoding import KikuchiHamiltonian, KikuchiMatrixEntry, KikuchiNonZeroIndex
from .kikuchi_guiding_state import GuidingState, SimpleGuidingState
from .kxor_instance import Constraint, KXorInstance
+from .planted_noisy_kxor import AliceTheorem, PlantedNoisyKXOR
diff --git a/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/__init__.py b/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/__init__.py
new file mode 100644
index 000000000..09dfda120
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/__init__.py
@@ -0,0 +1,15 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+from .guided_hamiltonian import GuidedHamiltonian, GuidedHamiltonianPhaseEstimation
+from .walk_operator import QubitizedWalkOperator
diff --git a/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/guided_hamiltonian.ipynb b/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/guided_hamiltonian.ipynb
new file mode 100644
index 000000000..f8a5eb2d0
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/guided_hamiltonian.ipynb
@@ -0,0 +1,311 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "e299e7a9",
+ "metadata": {
+ "cq.autogen": "title_cell"
+ },
+ "source": [
+ "# Guided (sparse) Hamiltonian Problem\n",
+ "\n",
+ "Section 4.4.2 Simulating the Kikuchi Hamiltonian\n",
+ "\n",
+ "This module contains oracles to implement the block-encoding of the Kikuchi\n",
+ "Hamiltonian corresponding to an input k-XOR-SAT instance.\n",
+ "\n",
+ "References:\n",
+ " [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1)\n",
+ " Section 4.4.2 for algorithm. Section 2.4 for definitions and notation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "e2be674c",
+ "metadata": {
+ "cq.autogen": "top_imports"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran import Bloq, CompositeBloq, BloqBuilder, Signature, Register\n",
+ "from qualtran import QBit, QInt, QUInt, QAny\n",
+ "from qualtran.drawing import show_bloq, show_call_graph, show_counts_sigma\n",
+ "from typing import *\n",
+ "import numpy as np\n",
+ "import sympy\n",
+ "import cirq"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8d10248d",
+ "metadata": {
+ "cq.autogen": "GuidedHamiltonian.bloq_doc.md"
+ },
+ "source": [
+ "## `GuidedHamiltonian`\n",
+ "Solve the guided (sparse) hamiltonian problem.\n",
+ "\n",
+ "Definition 4.8 (modified to accept any block-encoding):\n",
+ "In the Guided Hamiltonian problem we are given the following as input:\n",
+ "\n",
+ "1. A $(\\sqrt{2} s, \\cdot, 0)$-block-encoding of a Hamiltonian $H$ such that $\\|H\\|_\\max \\le s$.\n",
+ "2. A unitary program that prepares $|\\Psi\\rangle|0^A\\rangle$.\n",
+ "3. Parameters $\\lambda \\in [-\\Lambda, \\Lambda]$, $\\alpha \\in (0, 1)$, $\\gamma \\in (0, 1]$.\n",
+ "\n",
+ "and we should output\n",
+ "\n",
+ "- YES (1) if $\\| \\Pi_{\\ge \\lambda} (H) |\\Psi\\rangle \\| \\ge \\gamma$\n",
+ "- NO (0) if $\\|H\\| \\le (1 - \\alpha) \\lambda$\n",
+ "\n",
+ "Note that the above drops the sparse requirement, and accepts any\n",
+ "$(\\alpha_H, \\cdot, \\cdot)$-block-encoding of $H$.\n",
+ "In the sparse Hamiltonian case, $\\alpha_H = s$ (where $s$ is the sparsity).\n",
+ "\n",
+ "Algorithm (Theorem 4.9):\n",
+ " This uses phase estimation on the block-encoding of $e^{iHt}$, and then uses\n",
+ " amplitude amplification to increase the success probability to $1 - o(1)$.\n",
+ "\n",
+ "We instead directly do phase-estimation on the qubitized (Szegedy) walk operator for $H$\n",
+ "\n",
+ "#### Parameters\n",
+ " - `hamiltonian`: the block-encoding of $H$\n",
+ " - `guiding_state`: the unitary that prepares $|\\Psi\\rangle$\n",
+ " - `lambd`: parameter $\\lambda$\n",
+ " - `alpha`: parameter $\\alpha$\n",
+ " - `gamma`: parameter $\\gamma$ \n",
+ "\n",
+ "#### References\n",
+ " - [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1). Section 4.2 \"Guided Sparse Hamiltonian Problem\".\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "29d536c3",
+ "metadata": {
+ "cq.autogen": "GuidedHamiltonian.bloq_doc.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.optimization.k_xor_sat.guided_hamiltonian import GuidedHamiltonian"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a216ac70",
+ "metadata": {
+ "cq.autogen": "GuidedHamiltonian.example_instances.md"
+ },
+ "source": [
+ "### Example Instances"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "fabf68e4",
+ "metadata": {
+ "cq.autogen": "GuidedHamiltonian.guided_hamiltonian"
+ },
+ "outputs": [],
+ "source": [
+ "import sympy\n",
+ "\n",
+ "from qualtran.bloqs.optimization.k_xor_sat import GuidingState, KikuchiHamiltonian, KXorInstance\n",
+ "from qualtran.bloqs.state_preparation.black_box_prepare import BlackBoxPrepare\n",
+ "from qualtran.symbolics import ceil, log2\n",
+ "\n",
+ "n, k, m, c = sympy.symbols(\"n k m c\", positive=True, integer=True)\n",
+ "zeta = sympy.symbols(r\"\\zeta\", positive=True)\n",
+ "\n",
+ "inst_guide = KXorInstance.symbolic(n, (1 - zeta) * m, k, max_rhs=2)\n",
+ "inst_solve = KXorInstance.symbolic(n, zeta * m, k, max_rhs=2)\n",
+ "l = c * k\n",
+ "s = l * ceil(log2(n))\n",
+ "\n",
+ "Psi = GuidingState(inst_guide, l)\n",
+ "H = KikuchiHamiltonian(inst_solve, c * k, s)\n",
+ "\n",
+ "lambd, alpha, gamma = sympy.symbols(r\"\\lambda \\alpha \\gamma\", positive=True, real=True)\n",
+ "guided_hamiltonian = GuidedHamiltonian(H, BlackBoxPrepare(Psi), lambd, alpha, gamma)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7ad9d994",
+ "metadata": {
+ "cq.autogen": "GuidedHamiltonian.graphical_signature.md"
+ },
+ "source": [
+ "#### Graphical Signature"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5ae17ad5",
+ "metadata": {
+ "cq.autogen": "GuidedHamiltonian.graphical_signature.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.drawing import show_bloqs\n",
+ "show_bloqs([guided_hamiltonian],\n",
+ " ['`guided_hamiltonian`'])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1b3e1663",
+ "metadata": {
+ "cq.autogen": "GuidedHamiltonian.call_graph.md"
+ },
+ "source": [
+ "### Call Graph"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "08946e48",
+ "metadata": {
+ "cq.autogen": "GuidedHamiltonian.call_graph.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.resource_counting.generalizers import ignore_split_join\n",
+ "guided_hamiltonian_g, guided_hamiltonian_sigma = guided_hamiltonian.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
+ "show_call_graph(guided_hamiltonian_g)\n",
+ "show_counts_sigma(guided_hamiltonian_sigma)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0b22b193",
+ "metadata": {
+ "cq.autogen": "GuidedHamiltonianPhaseEstimation.bloq_doc.md"
+ },
+ "source": [
+ "## `GuidedHamiltonianPhaseEstimation`\n",
+ "Implement the phase estimation algorithm $U_\\text{PE}$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "b3806eb0",
+ "metadata": {
+ "cq.autogen": "GuidedHamiltonianPhaseEstimation.bloq_doc.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.optimization.k_xor_sat.guided_hamiltonian import GuidedHamiltonianPhaseEstimation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "500f891d",
+ "metadata": {
+ "cq.autogen": "GuidedHamiltonianPhaseEstimation.example_instances.md"
+ },
+ "source": [
+ "### Example Instances"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "bfdbf9a6",
+ "metadata": {
+ "cq.autogen": "GuidedHamiltonianPhaseEstimation.guided_phase_estimate_symb"
+ },
+ "outputs": [],
+ "source": [
+ "import sympy\n",
+ "\n",
+ "from qualtran.bloqs.optimization.k_xor_sat import GuidingState, KikuchiHamiltonian, KXorInstance\n",
+ "from qualtran.bloqs.state_preparation.black_box_prepare import BlackBoxPrepare\n",
+ "from qualtran.symbolics import ceil, log2\n",
+ "\n",
+ "n, k, c = sympy.symbols(\"n k c\", positive=True, integer=True)\n",
+ "m_guide, m_solve = sympy.symbols(\"m_1 m_2\", positive=True, integer=True)\n",
+ "\n",
+ "inst_guide = KXorInstance.symbolic(n, m_guide, k, max_rhs=2)\n",
+ "inst_solve = KXorInstance.symbolic(n, m_solve, k, max_rhs=2)\n",
+ "l = c * k\n",
+ "s = l * ceil(log2(n))\n",
+ "\n",
+ "Psi = GuidingState(inst_guide, l)\n",
+ "H = KikuchiHamiltonian(inst_solve, c * k, s)\n",
+ "\n",
+ "eps, delta = sympy.symbols(r\"\\epsilon_{PE} \\delta_{PE}\", positive=True, real=True)\n",
+ "guided_phase_estimate_symb = GuidedHamiltonianPhaseEstimation(\n",
+ " H, BlackBoxPrepare(Psi), eps, delta\n",
+ ")\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d6408318",
+ "metadata": {
+ "cq.autogen": "GuidedHamiltonianPhaseEstimation.graphical_signature.md"
+ },
+ "source": [
+ "#### Graphical Signature"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "3a1d74b2",
+ "metadata": {
+ "cq.autogen": "GuidedHamiltonianPhaseEstimation.graphical_signature.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.drawing import show_bloqs\n",
+ "show_bloqs([guided_phase_estimate_symb],\n",
+ " ['`guided_phase_estimate_symb`'])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a5d710cd",
+ "metadata": {
+ "cq.autogen": "GuidedHamiltonianPhaseEstimation.call_graph.md"
+ },
+ "source": [
+ "### Call Graph"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "749b6440",
+ "metadata": {
+ "cq.autogen": "GuidedHamiltonianPhaseEstimation.call_graph.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.resource_counting.generalizers import ignore_split_join\n",
+ "guided_phase_estimate_symb_g, guided_phase_estimate_symb_sigma = guided_phase_estimate_symb.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
+ "show_call_graph(guided_phase_estimate_symb_g)\n",
+ "show_counts_sigma(guided_phase_estimate_symb_sigma)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "name": "python"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/guided_hamiltonian.py b/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/guided_hamiltonian.py
new file mode 100644
index 000000000..b7a342f1a
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/guided_hamiltonian.py
@@ -0,0 +1,345 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+"""Section 4.4.2 Simulating the Kikuchi Hamiltonian
+
+This module contains oracles to implement the block-encoding of the Kikuchi
+Hamiltonian corresponding to an input k-XOR-SAT instance.
+
+References:
+ [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1)
+ Section 4.4.2 for algorithm. Section 2.4 for definitions and notation.
+"""
+from collections import Counter
+from functools import cached_property
+
+from attrs import frozen
+
+from qualtran import (
+ Bloq,
+ bloq_example,
+ BloqBuilder,
+ BloqDocSpec,
+ DecomposeTypeError,
+ QAny,
+ Signature,
+ Soquet,
+ SoquetT,
+)
+from qualtran.bloqs.block_encoding import BlockEncoding
+from qualtran.bloqs.phase_estimation import KaiserWindowState, QubitizationQPE
+from qualtran.bloqs.phase_estimation.qpe_window_state import QPEWindowStateBase
+from qualtran.bloqs.reflections.prepare_identity import PrepareIdentity
+from qualtran.bloqs.reflections.reflection_using_prepare import ReflectionUsingPrepare
+from qualtran.bloqs.state_preparation.black_box_prepare import BlackBoxPrepare
+from qualtran.resource_counting import BloqCountDictT, SympySymbolAllocator
+from qualtran.symbolics import ceil, is_symbolic, is_zero, ln, log2, pi, SymbolicFloat, SymbolicInt
+
+from .walk_operator import QubitizedWalkOperator
+
+
+@frozen
+class GuidedHamiltonianPhaseEstimation(Bloq):
+ r"""Implement the phase estimation algorithm $U_\text{PE}$"""
+
+ hamiltonian: BlockEncoding
+ guiding_state: BlackBoxPrepare
+ precision: SymbolicFloat
+ fail_prob: SymbolicFloat
+
+ def __attrs_post_init__(self):
+ assert (
+ self.hamiltonian.resource_bitsize == 0
+ ), "block encoding with resource regs not supported"
+
+ assert self.hamiltonian.system_bitsize == self.guiding_state.selection_bitsize
+
+ @cached_property
+ def signature(self) -> 'Signature':
+ return Signature.build_from_dtypes(
+ phase_estimate=self.qpe_window_state.m_register.dtype,
+ system=QAny(self.hamiltonian.system_bitsize),
+ walk_ancilla=QAny(self.hamiltonian.ancilla_bitsize),
+ guide_ancilla=QAny(self.guiding_state.junk_bitsize),
+ )
+
+ @cached_property
+ def walk_operator(self) -> QubitizedWalkOperator:
+ return QubitizedWalkOperator(self.hamiltonian)
+
+ @cached_property
+ def qpe_window_state(self) -> QPEWindowStateBase:
+ """Kaiser Window state.
+ Computes a slightly larger value for a simpler expression.
+ https://arxiv.org/abs/2209.13581, Eq D14, D15
+ """
+ eps, delta = self.precision, self.fail_prob
+
+ alpha = ln(1 / delta) / pi(delta)
+
+ N = (1 / eps) * ln(1 / delta)
+ m_bits = ceil(log2(N))
+ return KaiserWindowState(bitsize=m_bits, alpha=alpha)
+
+ @cached_property
+ def qpe_bloq(self) -> QubitizationQPE:
+ return QubitizationQPE(self.walk_operator, self.qpe_window_state) # type: ignore
+
+ def build_composite_bloq(
+ self,
+ bb: 'BloqBuilder',
+ phase_estimate: Soquet,
+ system: Soquet,
+ walk_ancilla: Soquet,
+ **soqs: SoquetT,
+ ) -> dict[str, 'SoquetT']:
+
+ # prepare the guiding state
+ if is_zero(self.guiding_state.junk_bitsize):
+ system = bb.add(self.guiding_state, selection=system)
+ else:
+ system, guide_ancilla = bb.add(
+ self.guiding_state, selection=system, junk=soqs.pop('guide_ancilla')
+ )
+ soqs['guide_ancilla'] = guide_ancilla
+
+ # apply QPE
+ phase_estimate, system, walk_ancilla = bb.add(
+ self.qpe_bloq, qpe_reg=phase_estimate, system=system, ancilla=walk_ancilla
+ )
+
+ return {
+ 'phase_estimate': phase_estimate,
+ 'system': system,
+ 'walk_ancilla': walk_ancilla,
+ } | soqs
+
+
+@bloq_example
+def _guided_phase_estimate_symb() -> GuidedHamiltonianPhaseEstimation:
+ import sympy
+
+ from qualtran.bloqs.optimization.k_xor_sat import GuidingState, KikuchiHamiltonian, KXorInstance
+ from qualtran.bloqs.state_preparation.black_box_prepare import BlackBoxPrepare
+ from qualtran.symbolics import ceil, log2
+
+ n, k, c = sympy.symbols("n k c", positive=True, integer=True)
+ m_guide, m_solve = sympy.symbols("m_1 m_2", positive=True, integer=True)
+
+ inst_guide = KXorInstance.symbolic(n, m_guide, k, max_rhs=2)
+ inst_solve = KXorInstance.symbolic(n, m_solve, k, max_rhs=2)
+ l = c * k
+ s = l * ceil(log2(n))
+
+ Psi = GuidingState(inst_guide, l)
+ H = KikuchiHamiltonian(inst_solve, c * k, s)
+
+ eps, delta = sympy.symbols(r"\epsilon_{PE} \delta_{PE}", positive=True, real=True)
+ guided_phase_estimate_symb = GuidedHamiltonianPhaseEstimation(
+ H, BlackBoxPrepare(Psi), eps, delta
+ )
+
+ return guided_phase_estimate_symb
+
+
+_GUIDED_HAMILTONIAN_PHASE_ESTIMATION_DOC = BloqDocSpec(
+ bloq_cls=GuidedHamiltonianPhaseEstimation, examples=[_guided_phase_estimate_symb]
+)
+
+
+@frozen
+class GuidedHamiltonian(Bloq):
+ r"""Solve the guided (sparse) hamiltonian problem.
+
+ Definition 4.8 (modified to accept any block-encoding):
+ In the Guided Hamiltonian problem we are given the following as input:
+
+ 1. A $(\sqrt{2} s, \cdot, 0)$-block-encoding of a Hamiltonian $H$ such that $\|H\|_\max \le s$.
+ 2. A unitary program that prepares $|\Psi\rangle|0^A\rangle$.
+ 3. Parameters $\lambda \in [-\Lambda, \Lambda]$, $\alpha \in (0, 1)$, $\gamma \in (0, 1]$.
+
+ and we should output
+
+ - YES (1) if $\| \Pi_{\ge \lambda} (H) |\Psi\rangle \| \ge \gamma$
+ - NO (0) if $\|H\| \le (1 - \alpha) \lambda$
+
+ Note that the above drops the sparse requirement, and accepts any
+ $(\alpha_H, \cdot, \cdot)$-block-encoding of $H$.
+ In the sparse Hamiltonian case, $\alpha_H = s$ (where $s$ is the sparsity).
+
+ Algorithm (Theorem 4.9):
+ This uses phase estimation on the block-encoding of $e^{iHt}$, and then uses
+ amplitude amplification to increase the success probability to $1 - o(1)$.
+
+ We instead directly do phase-estimation on the qubitized (Szegedy) walk operator for $H$
+
+ Args:
+ hamiltonian: the block-encoding of $H$
+ guiding_state: the unitary that prepares $|\Psi\rangle$
+ lambd: parameter $\lambda$
+ alpha: parameter $\alpha$
+ gamma: parameter $\gamma$
+
+ References:
+ [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1)
+ Section 4.2 "Guided Sparse Hamiltonian Problem".
+ """
+
+ hamiltonian: BlockEncoding
+ guiding_state: BlackBoxPrepare
+ lambd: SymbolicFloat
+ alpha: SymbolicFloat
+ gamma: SymbolicFloat
+
+ def __attrs_post_init__(self):
+ assert self.hamiltonian.resource_bitsize == 0, "resource not supported"
+ assert (
+ self.hamiltonian.system_bitsize == self.guiding_state.selection_bitsize
+ ), "system registers must match"
+
+ assert self.signature == self.qpe_bloq.signature
+
+ @cached_property
+ def signature(self) -> 'Signature':
+ return Signature.build_from_dtypes(
+ phase_estimate=self.qpe_bloq.qpe_window_state.m_register.dtype,
+ system=QAny(self.hamiltonian.system_bitsize),
+ walk_ancilla=QAny(self.hamiltonian.ancilla_bitsize),
+ guide_ancilla=QAny(self.guiding_state.junk_bitsize),
+ )
+
+ @cached_property
+ def qpe_precision(self) -> SymbolicFloat:
+ r"""The precision for phase estimation.
+
+ Page 31, Eq 100 of the reference gives the precision value for estimating phases
+ of $e^{iHt}$ with $t = \pi/(2s)$. But this bloq does phase estimation directly
+ on the walk operator, with eigenphases $e^{-i \arccos(H/s)}$.
+
+ To bound this, consider the two eigenvalues that are to be distinguished:
+ $\lambda$ and $(1 - \alpha)\lambda$. We can bound the difference in estimated phases as
+
+ $$
+ |\arccos(\lambda / s) - \arccos((1-\alpha)\lambda / s)|
+ \le \frac{\alpha \lambda}{s} \frac{1}{1 - ((1 - \alpha)\lambda / s)^2}
+ $$
+
+ As we know $\|H\| \le s/\sqrt{2}$, it means $\lambda/s \le 1/\sqrt{2}$,
+ therefore the second term is at most $\sqrt{2}$.
+
+ In the sparse encoding case, we can increase the sparsity to $\sqrt{2} s$
+ when block-encoding the input, to ensure that we have an epsilon bound of
+ $\alpha \lambda / s$.
+ """
+ return self.alpha * self.lambd / self.hamiltonian.alpha
+
+ @cached_property
+ def qpe_fail_prob(self) -> SymbolicFloat:
+ """Page 31, above Eq 104."""
+ return self.gamma**3
+
+ @cached_property
+ def n_rounds_amplification(self) -> SymbolicInt:
+ return ceil(1 / self.gamma)
+
+ @cached_property
+ def qpe_bloq(self) -> GuidedHamiltonianPhaseEstimation:
+ return GuidedHamiltonianPhaseEstimation(
+ hamiltonian=self.hamiltonian,
+ guiding_state=self.guiding_state,
+ precision=self.qpe_precision,
+ fail_prob=self.qpe_fail_prob,
+ )
+
+ @cached_property
+ def _refl_guide_ancilla(self) -> ReflectionUsingPrepare:
+ return ReflectionUsingPrepare.reflection_around_zero(
+ bitsizes=[self.guiding_state.junk_bitsize], global_phase=-1
+ )
+
+ @cached_property
+ def _refl_all(self) -> ReflectionUsingPrepare:
+ return ReflectionUsingPrepare(PrepareIdentity(tuple(self.signature)), global_phase=-1)
+
+ def build_composite_bloq(self, bb: 'BloqBuilder', **soqs: 'SoquetT') -> dict[str, 'SoquetT']:
+ if is_symbolic(self.n_rounds_amplification):
+ raise DecomposeTypeError(
+ f'cannot decompose {self} with symbolic number of rounds {self.n_rounds_amplification}'
+ )
+
+ soqs = bb.add_d(self.qpe_bloq, **soqs)
+ for _ in range(self.n_rounds_amplification):
+ ### reflect about bad state
+ soqs['guide_ancilla'] = bb.add(self._refl_guide_ancilla, reg0_=soqs['guide_ancilla'])
+
+ ### reflect about prepared state
+ soqs = bb.add_d(self.qpe_bloq.adjoint(), **soqs)
+ soqs = bb.add_d(self._refl_all, **soqs)
+ soqs = bb.add_d(self.qpe_bloq, **soqs)
+
+ return soqs
+
+ def build_call_graph(self, ssa: 'SympySymbolAllocator') -> BloqCountDictT:
+ counts = Counter[Bloq]()
+
+ # prepare the initial state
+ counts[self.qpe_bloq] += 1
+
+ # reflect about the ancilla being all 0
+ counts[self._refl_guide_ancilla] += self.n_rounds_amplification
+
+ # reflect about the prepared state
+ counts[self.qpe_bloq.adjoint()] += self.n_rounds_amplification
+ counts[self._refl_all] += self.n_rounds_amplification
+ counts[self.qpe_bloq] += self.n_rounds_amplification
+
+ return counts
+
+
+@bloq_example
+def _guided_hamiltonian() -> GuidedHamiltonian:
+ import sympy
+
+ from qualtran.bloqs.optimization.k_xor_sat import GuidingState, KikuchiHamiltonian, KXorInstance
+ from qualtran.bloqs.state_preparation.black_box_prepare import BlackBoxPrepare
+ from qualtran.symbolics import ceil, log2
+
+ n, k, m, c = sympy.symbols("n k m c", positive=True, integer=True)
+ zeta = sympy.symbols(r"\zeta", positive=True)
+
+ inst_guide = KXorInstance.symbolic(n, (1 - zeta) * m, k, max_rhs=2)
+ inst_solve = KXorInstance.symbolic(n, zeta * m, k, max_rhs=2)
+ l = c * k
+ s = l * ceil(log2(n))
+
+ Psi = GuidingState(inst_guide, l)
+ H = KikuchiHamiltonian(inst_solve, c * k, s)
+
+ lambd, alpha, gamma = sympy.symbols(r"\lambda \alpha \gamma", positive=True, real=True)
+ guided_hamiltonian = GuidedHamiltonian(H, BlackBoxPrepare(Psi), lambd, alpha, gamma)
+ return guided_hamiltonian
+
+
+_GUIDED_HAMILTONIAN_DOC = BloqDocSpec(bloq_cls=GuidedHamiltonian, examples=[_guided_hamiltonian])
diff --git a/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/guided_hamiltonian_test.py b/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/guided_hamiltonian_test.py
new file mode 100644
index 000000000..1ab6c5465
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/guided_hamiltonian_test.py
@@ -0,0 +1,31 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+import pytest
+
+from .guided_hamiltonian import _guided_hamiltonian, _guided_phase_estimate_symb
+
+
+@pytest.mark.parametrize("bloq_ex", [_guided_hamiltonian, _guided_phase_estimate_symb])
+def test_examples(bloq_autotester, bloq_ex):
+ if bloq_autotester.check_name == 'serialize':
+ pytest.skip()
+
+ bloq_autotester(bloq_ex)
+
+
+@pytest.mark.notebook
+def test_notebook():
+ from qualtran.testing import execute_notebook
+
+ execute_notebook('guided_hamiltonian')
diff --git a/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/tutorial_guided_hamiltonian.ipynb b/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/tutorial_guided_hamiltonian.ipynb
new file mode 100644
index 000000000..fe31ae38e
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/tutorial_guided_hamiltonian.ipynb
@@ -0,0 +1,2005 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "6d27900d7109a493",
+ "metadata": {},
+ "source": [
+ "# Guided (sparse) Hamiltonian Problem"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "id": "ec7403af5f8f9302",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-08-27T18:07:47.146430Z",
+ "start_time": "2024-08-27T18:07:44.824865Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from attrs import frozen\n",
+ "import attrs\n",
+ "from qualtran import Bloq, Signature, Register, QAny\n",
+ "from qualtran.drawing import show_bloq, show_call_graph, show_counts_sigma\n",
+ "from qualtran.symbolics import SymbolicInt, ceil, log2, ln, is_symbolic\n",
+ "from qualtran.resource_counting import big_O\n",
+ "from qualtran.resource_counting.generalizers import ignore_alloc_free, ignore_split_join, ignore_cliffords\n",
+ "from qualtran.bloqs.block_encoding import BlockEncoding\n",
+ "from qualtran.bloqs.reflections.reflection_using_prepare import ReflectionUsingPrepare\n",
+ "from qualtran.bloqs.max_k_xor_sat.guided_hamiltonian import GuidedHamiltonian\n",
+ "from qualtran.bloqs.max_k_xor_sat.shims import ArbitraryGate # arbitrary 1/2-qubit gate, for costing."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "fd4d302a-8cfe-48b5-8e44-a9b99a0b5e5b",
+ "metadata": {},
+ "source": [
+ "## `GuidedHamiltonian`\n",
+ "Solve the guided (sparse) hamiltonian problem.\n",
+ "\n",
+ "Definition 4.8 (modified with sparsity generalized to any):\n",
+ "In the Guided Hamiltonian problem we are given the following as input:\n",
+ "\n",
+ "1. A Hamiltonian $H$ with $\\|H\\|_\\max \\le 1$, specified via a block-encoding.\n",
+ "2. A unitary program that takes $|0^N\\rangle|0^A\\rangle$ and prepares $|\\Psi\\rangle|0^A\\rangle$.\n",
+ "3. Parameters $\\lambda \\in [-\\Lambda, \\Lambda]$, $\\alpha \\in (0, 1)$, $\\gamma \\in (0, 1]$.\n",
+ "\n",
+ "and we should output\n",
+ "\n",
+ "- YES if $\\| \\Pi_{\\ge \\lambda} (H) |\\Psi\\rangle \\| \\ge \\gamma$\n",
+ "- NO if $\\|H\\| \\le (1 - \\alpha) \\lambda$\n",
+ "\n",
+ "Note that the above drops the sparse requirement, and accepts any\n",
+ "$(\\alpha_H, \\cdot, \\cdot)$-block-encoding of $H$.\n",
+ "In the sparse Hamiltonian case, $\\alpha_H = s$ (where $s$ is the sparsity).\n",
+ "\n",
+ "Algorithm (Theorem 4.9):\n",
+ " This uses phase estimation on the block-encoding of $e^{iHt}$, and then uses\n",
+ " amplitude amplification to increase the success probability to $1 - o(1)$.\n",
+ "\n",
+ "We instead directly do phase-estimation on the qubitized (Szegedy) walk operator for $H$.\n",
+ "\n",
+ "#### Parameters\n",
+ " - `hamiltonian`: the block-encoding of $H$\n",
+ " - `guiding_state`: the unitary that prepares $|\\Psi\\rangle$\n",
+ " - `lambd`: parameter $\\lambda$\n",
+ " - `alpha`: parameter $\\alpha$\n",
+ " - `gamma`: parameter $\\gamma$ "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "06cdbc3b-b4bd-47da-84ba-cd7b0059bb6f",
+ "metadata": {},
+ "source": [
+ "# Computing Query Costs with Qualtran\n",
+ "\n",
+ "We will first create black-boxes for a Hamiltonian and a guiding state preparation, that can be passed to the `GuidedHamiltonian` bloq to count number of queries and gates."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "fb7db14a-d5d1-4f02-b082-43ada6fa1aee",
+ "metadata": {},
+ "source": [
+ "## Building black-box oracles"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b50f74cc-e8dc-4214-a020-af0e80ef5469",
+ "metadata": {},
+ "source": [
+ "### Graph oracles for the Hamiltonian\n",
+ "We first build the oracles $O_F$ and $O_H$, and use them to block-encode a sparse matrix."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "id": "4a490bf8-e83f-497a-a422-2e1eb2444e70",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "@frozen\n",
+ "class oracle_O_H(Bloq):\n",
+ " \"\"\"given (i, j), output H_{i, j}\"\"\"\n",
+ " N: SymbolicInt\n",
+ " entry_bits: SymbolicInt\n",
+ " \n",
+ " @property\n",
+ " def signature(self):\n",
+ " return Signature.build(i=self.N, j=self.N, entry=self.entry_bits)\n",
+ "\n",
+ " def adjoint(self):\n",
+ " return self\n",
+ "\n",
+ "@frozen\n",
+ "class oracle_O_F(Bloq):\n",
+ " \"\"\"Given (i, k), output (i, f(i, k)) s.t. f(i, k) is the k-th non zero entry in row i\"\"\"\n",
+ " N: SymbolicInt\n",
+ " reverse: bool = False\n",
+ " \n",
+ " @property\n",
+ " def signature(self):\n",
+ " return Signature.build(i=self.N, k=self.N)\n",
+ "\n",
+ " def adjoint(self):\n",
+ " return oracle_O_F(self.N, reverse=not self.reverse)\n",
+ "\n",
+ "\n",
+ "@frozen\n",
+ "class EncodeSparseHamiltonian(BlockEncoding):\n",
+ " \"\"\"(s, N+1, 0)-block-encoding of s-sparse NxN matrix H\"\"\"\n",
+ " N: SymbolicInt\n",
+ " s: SymbolicInt # sparsity\n",
+ " O_F: oracle_O_F\n",
+ " O_H: oracle_O_H\n",
+ "\n",
+ " @property\n",
+ " def signature(self) -> Signature:\n",
+ " return Signature.build_from_dtypes(\n",
+ " system=QAny(self.system_bitsize),\n",
+ " ancilla=QAny(self.ancilla_bitsize),\n",
+ " )\n",
+ "\n",
+ " @property\n",
+ " def system_bitsize(self):\n",
+ " return self.N\n",
+ "\n",
+ " @property\n",
+ " def ancilla_bitsize(self):\n",
+ " return self.N + 1\n",
+ "\n",
+ " @property\n",
+ " def resource_bitsize(self):\n",
+ " return 0\n",
+ "\n",
+ " @property\n",
+ " def alpha(self):\n",
+ " return self.s\n",
+ "\n",
+ " @property\n",
+ " def epsilon(self):\n",
+ " return 0\n",
+ "\n",
+ " @property\n",
+ " def signal_state(self):\n",
+ " from qualtran.bloqs.reflections.prepare_identity import PrepareIdentity\n",
+ " from qualtran.bloqs.state_preparation.black_box_prepare import BlackBoxPrepare\n",
+ " \n",
+ " return BlackBoxPrepare(PrepareIdentity.from_bitsizes([self.ancilla_bitsize]))\n",
+ "\n",
+ " def build_call_graph(self, ssa):\n",
+ " \"\"\"\n",
+ " References:\n",
+ " [Lecture Notes on Quantum Algorithms for Scientific Computation](https://arxiv.org/abs/2201.08309). Lin Lin (2022). Ch. 6.5.\n",
+ " \"\"\"\n",
+ " log_s = ceil(log2(self.s))\n",
+ " return {(self.O_F, 2), (self.O_H, 2), (ArbitraryGate(), 2*log_s)}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "60df1af0-0a6f-4645-8739-b75f4ece3553",
+ "metadata": {},
+ "source": [
+ "### State-preparation Oracle for the guiding state\n",
+ "\n",
+ "Point 2. Quantum circuit that uses $G$ gates and maps $|0^N\\rangle|0^A\\rangle$ to $|\\Psi\\rangle|0^A\\rangle$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "id": "0a17eab5-0a44-4526-9b08-483086c655bf",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "@frozen\n",
+ "class GuidingState(Bloq):\n",
+ " \"\"\"Point 2. Quantum circuit that uses G gates and maps |0^N>|0^A> to |\\Psi>|0^A>\"\"\"\n",
+ " N: SymbolicInt\n",
+ " A: SymbolicInt\n",
+ " G: SymbolicInt\n",
+ " \n",
+ " @property\n",
+ " def signature(self) -> Bloq:\n",
+ " return Signature.build(selection=self.N, junk=self.A)\n",
+ "\n",
+ " def build_call_graph(self, ssa):\n",
+ " return {(ArbitraryGate(), self.G)}\n",
+ " \n",
+ " @property\n",
+ " def selection_bitsize(self):\n",
+ " return self.N\n",
+ " @property\n",
+ " def junk_bitsize(self):\n",
+ " return self.A\n",
+ " @property\n",
+ " def selection_registers(self):\n",
+ " return (Register('selection', QAny(self.N)),)\n",
+ " @property\n",
+ " def junk_registers(self):\n",
+ " return (Register('junk', QAny(self.A)),)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f127675c-6616-43eb-b33a-479ae146dcfa",
+ "metadata": {},
+ "source": [
+ "## An example invocation\n",
+ "With these oracles in place, we can now invoke the `GuidedHamiltonian` algorithm."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "id": "32219420-f41b-4c80-b89b-2076795d596f",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import sympy\n",
+ "\n",
+ "def example_bloq() -> GuidedHamiltonian:\n",
+ " N, A, G, s = sympy.symbols(\"N A G s\", positive=True, integer=True)\n",
+ " lambd, alpha, gamma = sympy.symbols(r\"\\lambda \\alpha \\gamma\", positive=True, real=True)\n",
+ "\n",
+ " O_F = oracle_O_F(N)\n",
+ " O_H = oracle_O_H(N, 10)\n",
+ " be_H = EncodeSparseHamiltonian(N, s, O_F, O_H)\n",
+ " psi = GuidingState(N, A, G)\n",
+ "\n",
+ " return GuidedHamiltonian(be_H, psi, lambd, alpha, gamma)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "id": "13b8eb29-1af9-4d65-a954-cf96498efad1",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"453pt\" height=\"206pt\" viewBox=\"0.00 0.00 453.00 206.00\">\n",
+ "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 202)\">\n",
+ "<title>my_graph</title>\n",
+ "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-202 449,-202 449,4 -4,4\"/>\n",
+ "<!-- phase_estimate_G9 -->\n",
+ "<g id=\"node1\" class=\"node\">\n",
+ "<title>phase_estimate_G9</title>\n",
+ "<text text-anchor=\"middle\" x=\"63.5\" y=\"-175.32\" font-family=\"Times,serif\" font-size=\"14.00\">phase_estimate</text>\n",
+ "</g>\n",
+ "<!-- GuidedHamiltonian -->\n",
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+ "<text text-anchor=\"start\" x=\"179.38\" y=\"-82.7\" font-family=\"Times,serif\" font-size=\"14.00\">walk_ancilla</text>\n",
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+ "<text text-anchor=\"start\" x=\"176\" y=\"-59.7\" font-family=\"Times,serif\" font-size=\"14.00\">guide_ancilla</text>\n",
+ "</g>\n",
+ "<!-- phase_estimate_G9->GuidedHamiltonian -->\n",
+ "<g id=\"edge1\" class=\"edge\">\n",
+ "<title>phase_estimate_G9:e->GuidedHamiltonian:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M127,-180C152.38,-180 138.76,-137.06 161.09,-133.71\"/>\n",
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+ "<text text-anchor=\"middle\" x=\"145.5\" y=\"-161.25\" font-family=\"Times,serif\" font-size=\"10.00\">ceiling(lo ...</text>\n",
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+ "<!-- system_G11 -->\n",
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+ "<title>system_G11</title>\n",
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+ "<g id=\"node3\" class=\"node\">\n",
+ "<title>walk_ancilla_G0</title>\n",
+ "<text text-anchor=\"middle\" x=\"63.5\" y=\"-67.33\" font-family=\"Times,serif\" font-size=\"14.00\">walk_ancilla</text>\n",
+ "</g>\n",
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+ "<g id=\"edge3\" class=\"edge\">\n",
+ "<title>walk_ancilla_G0:e->GuidedHamiltonian:w</title>\n",
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+ "<title>guide_ancilla_G8</title>\n",
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+ "<g id=\"edge4\" class=\"edge\">\n",
+ "<title>guide_ancilla_G8:e->GuidedHamiltonian:w</title>\n",
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+ "</g>\n",
+ "<!-- phase_estimate_G2 -->\n",
+ "<g id=\"node6\" class=\"node\">\n",
+ "<title>phase_estimate_G2</title>\n",
+ "<text text-anchor=\"middle\" x=\"381.5\" y=\"-175.32\" font-family=\"Times,serif\" font-size=\"14.00\">phase_estimate</text>\n",
+ "</g>\n",
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+ "<g id=\"edge5\" class=\"edge\">\n",
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+ "<title>system_G7</title>\n",
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+ "</g>\n",
+ "<!-- GuidedHamiltonian->system_G7 -->\n",
+ "<g id=\"edge6\" class=\"edge\">\n",
+ "<title>GuidedHamiltonian:e->system_G7:w</title>\n",
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+ "</g>\n",
+ "<!-- walk_ancilla_G3 -->\n",
+ "<g id=\"node8\" class=\"node\">\n",
+ "<title>walk_ancilla_G3</title>\n",
+ "<text text-anchor=\"middle\" x=\"381.5\" y=\"-67.33\" font-family=\"Times,serif\" font-size=\"14.00\">walk_ancilla</text>\n",
+ "</g>\n",
+ "<!-- GuidedHamiltonian->walk_ancilla_G3 -->\n",
+ "<g id=\"edge7\" class=\"edge\">\n",
+ "<title>GuidedHamiltonian:e->walk_ancilla_G3:w</title>\n",
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+ "</g>\n",
+ "<!-- guide_ancilla_G4 -->\n",
+ "<g id=\"node9\" class=\"node\">\n",
+ "<title>guide_ancilla_G4</title>\n",
+ "<text text-anchor=\"middle\" x=\"381.5\" y=\"-13.32\" font-family=\"Times,serif\" font-size=\"14.00\">guide_ancilla</text>\n",
+ "</g>\n",
+ "<!-- GuidedHamiltonian->guide_ancilla_G4 -->\n",
+ "<g id=\"edge8\" class=\"edge\">\n",
+ "<title>GuidedHamiltonian:e->guide_ancilla_G4:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M281,-64.5C308.76,-64.5 298.1,-21.21 323.17,-18.17\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"324.55\" cy=\"-18.09\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"299.5\" y=\"-55.25\" font-family=\"Times,serif\" font-size=\"10.00\">A</text>\n",
+ "</g>\n",
+ "</g>\n",
+ "</svg>"
+ ],
+ "text/plain": [
+ "<IPython.core.display.SVG object>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "bloq = example_bloq()\n",
+ "show_bloq(bloq)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ac277b8a-8ae9-47cc-bd46-7f23c56d1392",
+ "metadata": {},
+ "source": [
+ "## Circuit Diagrams\n",
+ "\n",
+ "We will now look at the decomposition of the bloq, to see the steps of the algorithm.\n",
+ "First we look at the phase estimation bloq $U_\\text{PE}$.\n",
+ "To obtain the entire algorithm, we use amplitude-amplification on $U_\\text{PE}$ for $O(1/\\gamma)$ rounds.\n",
+ "The good subspace is characterized by `guide_ancilla` being all 0."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "id": "9d2c34d3-9a19-4d54-a60a-549c590533e7",
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
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+ "</g>\n",
+ "<!-- walk_ancilla -->\n",
+ "<g id=\"node3\" class=\"node\">\n",
+ "<title>walk_ancilla</title>\n",
+ "<text text-anchor=\"middle\" x=\"63.5\" y=\"-127.33\" font-family=\"Times,serif\" font-size=\"14.00\">walk_ancilla</text>\n",
+ "</g>\n",
+ "<!-- walk_ancilla->QubitizationQPE -->\n",
+ "<g id=\"edge5\" class=\"edge\">\n",
+ "<title>walk_ancilla:e->QubitizationQPE:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M115.58,-132C185.14,-132 202.99,-140.76 271.14,-140.99\"/>\n",
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+ "</g>\n",
+ "<!-- guide_ancilla_G7 -->\n",
+ "<g id=\"node4\" class=\"node\">\n",
+ "<title>guide_ancilla_G7</title>\n",
+ "<text text-anchor=\"middle\" x=\"63.5\" y=\"-13.32\" font-family=\"Times,serif\" font-size=\"14.00\">guide_ancilla</text>\n",
+ "</g>\n",
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+ "<title>guide_ancilla_G7:e->GuidingState:w</title>\n",
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+ "<!-- GuidingState->QubitizationQPE -->\n",
+ "<g id=\"edge4\" class=\"edge\">\n",
+ "<title>GuidingState:e->QubitizationQPE:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M237,-66.5C282.44,-66.5 229.79,-160.23 271.4,-163.89\"/>\n",
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+ "</g>\n",
+ "<!-- guide_ancilla -->\n",
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+ "<title>guide_ancilla</title>\n",
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+ "<title>GuidingState:e->guide_ancilla:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M237,-43.5C312.57,-43.5 332.13,-43.99 406.39,-44\"/>\n",
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+ "<title>phase_estimate</title>\n",
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+ "</g>\n",
+ "<!-- QubitizationQPE->phase_estimate -->\n",
+ "<g id=\"edge6\" class=\"edge\">\n",
+ "<title>QubitizationQPE:e->phase_estimate:w</title>\n",
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+ "<!-- system_G3 -->\n",
+ "<g id=\"node8\" class=\"node\">\n",
+ "<title>system_G3</title>\n",
+ "<text text-anchor=\"middle\" x=\"464.5\" y=\"-159.32\" font-family=\"Times,serif\" font-size=\"14.00\">system</text>\n",
+ "</g>\n",
+ "<!-- QubitizationQPE->system_G3 -->\n",
+ "<g id=\"edge7\" class=\"edge\">\n",
+ "<title>QubitizationQPE:e->system_G3:w</title>\n",
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+ "</g>\n",
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+ "<g id=\"node9\" class=\"node\">\n",
+ "<title>walk_ancilla_G1</title>\n",
+ "<text text-anchor=\"middle\" x=\"464.5\" y=\"-105.33\" font-family=\"Times,serif\" font-size=\"14.00\">walk_ancilla</text>\n",
+ "</g>\n",
+ "<!-- QubitizationQPE->walk_ancilla_G1 -->\n",
+ "<g id=\"edge8\" class=\"edge\">\n",
+ "<title>QubitizationQPE:e->walk_ancilla_G1:w</title>\n",
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+ ],
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+ "<IPython.core.display.SVG object>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "show_bloq(bloq.qpe_bloq.decompose_bloq())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "08002b28-5d5f-4283-add6-d4fd914a0112",
+ "metadata": {},
+ "source": [
+ "### Full Circuit\n",
+ "For exposition, let us pick the number of rounds as a constant (say, $3$) to see the decomposition:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "id": "46e5a6af-4270-49fd-af5a-ae066503e378",
+ "metadata": {},
+ "outputs": [
+ {
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+ "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 202)\">\n",
+ "<title>my_graph</title>\n",
+ "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-202 3047,-202 3047,4 -4,4\"/>\n",
+ "<!-- phase_estimate_G52 -->\n",
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+ "<title>phase_estimate_G52</title>\n",
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+ "<title>ReflectAboutZero:e->GuidedHamiltonianPhaseEstimation_G37:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M2650,-110.5C2665.42,-110.5 2669.99,-110.5 2684.06,-110.5\"/>\n",
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+ "<text text-anchor=\"middle\" x=\"2668.5\" y=\"-113.25\" font-family=\"Times,serif\" font-size=\"10.00\">N</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero->GuidedHamiltonianPhaseEstimation_G37 -->\n",
+ "<g id=\"edge42\" class=\"edge\">\n",
+ "<title>ReflectAboutZero:e->GuidedHamiltonianPhaseEstimation_G37:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M2650,-87.5C2665.42,-87.5 2669.99,-87.5 2684.06,-87.5\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"2685.5\" cy=\"-87.5\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"2668.5\" y=\"-90.25\" font-family=\"Times,serif\" font-size=\"10.00\">N + 1</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero->GuidedHamiltonianPhaseEstimation_G37 -->\n",
+ "<g id=\"edge43\" class=\"edge\">\n",
+ "<title>ReflectAboutZero:e->GuidedHamiltonianPhaseEstimation_G37:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M2650,-64.5C2665.42,-64.5 2669.99,-64.5 2684.06,-64.5\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"2685.5\" cy=\"-64.5\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"2668.5\" y=\"-67.25\" font-family=\"Times,serif\" font-size=\"10.00\">A</text>\n",
+ "</g>\n",
+ "<!-- Adjoint_G27 -->\n",
+ "<g id=\"node13\" class=\"node\">\n",
+ "<title>Adjoint_G27</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"529,-145 529,-163 814,-163 814,-145 529,-145\"/>\n",
+ "<text text-anchor=\"start\" x=\"531.62\" y=\"-150.5\" font-family=\"Times,serif\" font-size=\"10.00\">Adjoint(subbloq=GuidedHamiltonianPhaseEstimation)</text>\n",
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+ "<polygon fill=\"none\" stroke=\"black\" points=\"529,-53 529,-76 814,-76 814,-53 529,-53\"/>\n",
+ "<text text-anchor=\"start\" x=\"625\" y=\"-59.7\" font-family=\"Times,serif\" font-size=\"14.00\">guide_ancilla</text>\n",
+ "</g>\n",
+ "<!-- GuidedHamiltonianPhaseEstimation_G18->Adjoint_G27 -->\n",
+ "<g id=\"edge6\" class=\"edge\">\n",
+ "<title>GuidedHamiltonianPhaseEstimation_G18:e->Adjoint_G27:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M356,-133.5C431.99,-133.5 451.65,-133.5 526.32,-133.5\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"527.5\" cy=\"-133.5\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"442.5\" y=\"-136.25\" font-family=\"Times,serif\" font-size=\"10.00\">ceiling(lo ...</text>\n",
+ "</g>\n",
+ "<!-- GuidedHamiltonianPhaseEstimation_G18->Adjoint_G27 -->\n",
+ "<g id=\"edge7\" class=\"edge\">\n",
+ "<title>GuidedHamiltonianPhaseEstimation_G18:e->Adjoint_G27:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M356,-110.5C431.99,-110.5 451.65,-110.5 526.32,-110.5\"/>\n",
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+ "<text text-anchor=\"middle\" x=\"442.5\" y=\"-113.25\" font-family=\"Times,serif\" font-size=\"10.00\">N</text>\n",
+ "</g>\n",
+ "<!-- GuidedHamiltonianPhaseEstimation_G18->Adjoint_G27 -->\n",
+ "<g id=\"edge8\" class=\"edge\">\n",
+ "<title>GuidedHamiltonianPhaseEstimation_G18:e->Adjoint_G27:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M356,-87.5C431.99,-87.5 451.65,-87.5 526.32,-87.5\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"527.5\" cy=\"-87.5\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"442.5\" y=\"-90.25\" font-family=\"Times,serif\" font-size=\"10.00\">N + 1</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G42 -->\n",
+ "<g id=\"node16\" class=\"node\">\n",
+ "<title>ReflectAboutZero_G42</title>\n",
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+ "<text text-anchor=\"start\" x=\"397.88\" y=\"-31\" font-family=\"Times,serif\" font-size=\"10.00\">ReflectAboutZero</text>\n",
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+ "<text text-anchor=\"start\" x=\"396\" y=\"-9.2\" font-family=\"Times,serif\" font-size=\"14.00\">guide_ancilla</text>\n",
+ "</g>\n",
+ "<!-- GuidedHamiltonianPhaseEstimation_G18->ReflectAboutZero_G42 -->\n",
+ "<g id=\"edge5\" class=\"edge\">\n",
+ "<title>GuidedHamiltonianPhaseEstimation_G18:e->ReflectAboutZero_G42:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M356,-64.5C382.85,-64.5 366.43,-17.49 390.23,-14.18\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"391.5\" cy=\"-14.1\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"374.5\" y=\"-43.25\" font-family=\"Times,serif\" font-size=\"10.00\">A</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G23->Adjoint -->\n",
+ "<g id=\"edge35\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G23:e->Adjoint:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M2174,-15C2200.5,-15 2184.74,-61.08 2208.27,-64.32\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"2209.5\" cy=\"-64.4\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"2192.5\" y=\"-44.25\" font-family=\"Times,serif\" font-size=\"10.00\">A</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G25->Adjoint_G9 -->\n",
+ "<g id=\"edge22\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G25:e->Adjoint_G9:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1333,-14C1359.85,-14 1343.43,-61.01 1367.23,-64.32\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"1368.5\" cy=\"-64.4\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"1351.5\" y=\"-43.25\" font-family=\"Times,serif\" font-size=\"10.00\">A</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G44 -->\n",
+ "<g id=\"node17\" class=\"node\">\n",
+ "<title>ReflectAboutZero_G44</title>\n",
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+ "<text text-anchor=\"start\" x=\"864.88\" y=\"-150.5\" font-family=\"Times,serif\" font-size=\"10.00\">ReflectAboutZero</text>\n",
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+ "<text text-anchor=\"start\" x=\"854\" y=\"-128.7\" font-family=\"Times,serif\" font-size=\"14.00\">phase_estimate</text>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"851,-99 851,-122 968,-122 968,-99 851,-99\"/>\n",
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+ "<text text-anchor=\"start\" x=\"866.38\" y=\"-82.7\" font-family=\"Times,serif\" font-size=\"14.00\">walk_ancilla</text>\n",
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+ "<text text-anchor=\"start\" x=\"863\" y=\"-59.7\" font-family=\"Times,serif\" font-size=\"14.00\">guide_ancilla</text>\n",
+ "</g>\n",
+ "<!-- Adjoint_G27->ReflectAboutZero_G44 -->\n",
+ "<g id=\"edge10\" class=\"edge\">\n",
+ "<title>Adjoint_G27:e->ReflectAboutZero_G44:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M814,-133.5C829.42,-133.5 833.99,-133.5 848.06,-133.5\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"849.5\" cy=\"-133.5\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"832.5\" y=\"-136.25\" font-family=\"Times,serif\" font-size=\"10.00\">ceiling(lo ...</text>\n",
+ "</g>\n",
+ "<!-- Adjoint_G27->ReflectAboutZero_G44 -->\n",
+ "<g id=\"edge11\" class=\"edge\">\n",
+ "<title>Adjoint_G27:e->ReflectAboutZero_G44:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M814,-110.5C829.42,-110.5 833.99,-110.5 848.06,-110.5\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"849.5\" cy=\"-110.5\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"832.5\" y=\"-113.25\" font-family=\"Times,serif\" font-size=\"10.00\">N</text>\n",
+ "</g>\n",
+ "<!-- Adjoint_G27->ReflectAboutZero_G44 -->\n",
+ "<g id=\"edge12\" class=\"edge\">\n",
+ "<title>Adjoint_G27:e->ReflectAboutZero_G44:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M814,-87.5C829.42,-87.5 833.99,-87.5 848.06,-87.5\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"849.5\" cy=\"-87.5\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"832.5\" y=\"-90.25\" font-family=\"Times,serif\" font-size=\"10.00\">N + 1</text>\n",
+ "</g>\n",
+ "<!-- Adjoint_G27->ReflectAboutZero_G44 -->\n",
+ "<g id=\"edge13\" class=\"edge\">\n",
+ "<title>Adjoint_G27:e->ReflectAboutZero_G44:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M814,-64.5C829.42,-64.5 833.99,-64.5 848.06,-64.5\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"849.5\" cy=\"-64.5\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"832.5\" y=\"-67.25\" font-family=\"Times,serif\" font-size=\"10.00\">A</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G32->GuidedHamiltonianPhaseEstimation -->\n",
+ "<g id=\"edge27\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G32:e->GuidedHamiltonianPhaseEstimation:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1809,-133.5C1824.42,-133.5 1828.99,-133.5 1843.06,-133.5\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"1844.5\" cy=\"-133.5\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"1827.5\" y=\"-136.25\" font-family=\"Times,serif\" font-size=\"10.00\">ceiling(lo ...</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G32->GuidedHamiltonianPhaseEstimation -->\n",
+ "<g id=\"edge28\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G32:e->GuidedHamiltonianPhaseEstimation:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1809,-110.5C1824.42,-110.5 1828.99,-110.5 1843.06,-110.5\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"1844.5\" cy=\"-110.5\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"1827.5\" y=\"-113.25\" font-family=\"Times,serif\" font-size=\"10.00\">N</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G32->GuidedHamiltonianPhaseEstimation -->\n",
+ "<g id=\"edge29\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G32:e->GuidedHamiltonianPhaseEstimation:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1809,-87.5C1824.42,-87.5 1828.99,-87.5 1843.06,-87.5\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"1844.5\" cy=\"-87.5\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"1827.5\" y=\"-90.25\" font-family=\"Times,serif\" font-size=\"10.00\">N + 1</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G32->GuidedHamiltonianPhaseEstimation -->\n",
+ "<g id=\"edge30\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G32:e->GuidedHamiltonianPhaseEstimation:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1809,-64.5C1824.42,-64.5 1828.99,-64.5 1843.06,-64.5\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"1844.5\" cy=\"-64.5\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"1827.5\" y=\"-67.25\" font-family=\"Times,serif\" font-size=\"10.00\">A</text>\n",
+ "</g>\n",
+ "<!-- phase_estimate_G75 -->\n",
+ "<g id=\"node18\" class=\"node\">\n",
+ "<title>phase_estimate_G75</title>\n",
+ "<text text-anchor=\"middle\" x=\"2979.5\" y=\"-175.32\" font-family=\"Times,serif\" font-size=\"14.00\">phase_estimate</text>\n",
+ "</g>\n",
+ "<!-- GuidedHamiltonianPhaseEstimation_G37->phase_estimate_G75 -->\n",
+ "<g id=\"edge44\" class=\"edge\">\n",
+ "<title>GuidedHamiltonianPhaseEstimation_G37:e->phase_estimate_G75:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M2879,-133.5C2904.38,-133.5 2890.76,-176.44 2913.09,-179.79\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"2914.5\" cy=\"-179.89\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"2897.5\" y=\"-161.25\" font-family=\"Times,serif\" font-size=\"10.00\">ceiling(lo ...</text>\n",
+ "</g>\n",
+ "<!-- system_G54 -->\n",
+ "<g id=\"node19\" class=\"node\">\n",
+ "<title>system_G54</title>\n",
+ "<text text-anchor=\"middle\" x=\"2979.5\" y=\"-121.33\" font-family=\"Times,serif\" font-size=\"14.00\">system</text>\n",
+ "</g>\n",
+ "<!-- GuidedHamiltonianPhaseEstimation_G37->system_G54 -->\n",
+ "<g id=\"edge45\" class=\"edge\">\n",
+ "<title>GuidedHamiltonianPhaseEstimation_G37:e->system_G54:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M2879,-110.5C2908.2,-110.5 2914.5,-125.05 2942.28,-125.96\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"2943.53\" cy=\"-125.98\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"2897.5\" y=\"-115.25\" font-family=\"Times,serif\" font-size=\"10.00\">N</text>\n",
+ "</g>\n",
+ "<!-- walk_ancilla_G51 -->\n",
+ "<g id=\"node20\" class=\"node\">\n",
+ "<title>walk_ancilla_G51</title>\n",
+ "<text text-anchor=\"middle\" x=\"2979.5\" y=\"-67.33\" font-family=\"Times,serif\" font-size=\"14.00\">walk_ancilla</text>\n",
+ "</g>\n",
+ "<!-- GuidedHamiltonianPhaseEstimation_G37->walk_ancilla_G51 -->\n",
+ "<g id=\"edge46\" class=\"edge\">\n",
+ "<title>GuidedHamiltonianPhaseEstimation_G37:e->walk_ancilla_G51:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M2879,-87.5C2900.71,-87.5 2904.54,-73.19 2924.86,-72.07\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"2925.92\" cy=\"-72.04\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"2897.5\" y=\"-85.25\" font-family=\"Times,serif\" font-size=\"10.00\">N + 1</text>\n",
+ "</g>\n",
+ "<!-- guide_ancilla_G81 -->\n",
+ "<g id=\"node21\" class=\"node\">\n",
+ "<title>guide_ancilla_G81</title>\n",
+ "<text text-anchor=\"middle\" x=\"2979.5\" y=\"-13.32\" font-family=\"Times,serif\" font-size=\"14.00\">guide_ancilla</text>\n",
+ "</g>\n",
+ "<!-- GuidedHamiltonianPhaseEstimation_G37->guide_ancilla_G81 -->\n",
+ "<g id=\"edge47\" class=\"edge\">\n",
+ "<title>GuidedHamiltonianPhaseEstimation_G37:e->guide_ancilla_G81:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M2879,-64.5C2906.76,-64.5 2896.1,-21.21 2921.17,-18.17\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"2922.55\" cy=\"-18.09\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"2897.5\" y=\"-55.25\" font-family=\"Times,serif\" font-size=\"10.00\">A</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G42->Adjoint_G27 -->\n",
+ "<g id=\"edge9\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G42:e->Adjoint_G27:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M492,-14C518.85,-14 502.43,-61.01 526.23,-64.32\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"527.5\" cy=\"-64.4\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"510.5\" y=\"-43.25\" font-family=\"Times,serif\" font-size=\"10.00\">A</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G44->GuidedHamiltonianPhaseEstimation_G4 -->\n",
+ "<g id=\"edge14\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G44:e->GuidedHamiltonianPhaseEstimation_G4:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M968,-133.5C983.42,-133.5 987.99,-133.5 1002.06,-133.5\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"1003.5\" cy=\"-133.5\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"986.5\" y=\"-136.25\" font-family=\"Times,serif\" font-size=\"10.00\">ceiling(lo ...</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G44->GuidedHamiltonianPhaseEstimation_G4 -->\n",
+ "<g id=\"edge15\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G44:e->GuidedHamiltonianPhaseEstimation_G4:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M968,-110.5C983.42,-110.5 987.99,-110.5 1002.06,-110.5\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"1003.5\" cy=\"-110.5\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"986.5\" y=\"-113.25\" font-family=\"Times,serif\" font-size=\"10.00\">N</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G44->GuidedHamiltonianPhaseEstimation_G4 -->\n",
+ "<g id=\"edge16\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G44:e->GuidedHamiltonianPhaseEstimation_G4:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M968,-87.5C983.42,-87.5 987.99,-87.5 1002.06,-87.5\"/>\n",
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+ "<text text-anchor=\"middle\" x=\"986.5\" y=\"-90.25\" font-family=\"Times,serif\" font-size=\"10.00\">N + 1</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G44->GuidedHamiltonianPhaseEstimation_G4 -->\n",
+ "<g id=\"edge17\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G44:e->GuidedHamiltonianPhaseEstimation_G4:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M968,-64.5C983.42,-64.5 987.99,-64.5 1002.06,-64.5\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"1003.5\" cy=\"-64.5\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"986.5\" y=\"-67.25\" font-family=\"Times,serif\" font-size=\"10.00\">A</text>\n",
+ "</g>\n",
+ "</g>\n",
+ "</svg>"
+ ],
+ "text/plain": [
+ "<IPython.core.display.SVG object>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "bloq_4_rounds = attrs.evolve(bloq, gamma=1/3)\n",
+ "show_bloq(bloq_4_rounds.decompose_bloq())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "id": "214f731f-22d8-4767-8b23-13ad1c400abf",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
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+ "<!-- phase_estimate_G62 -->\n",
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+ "<text text-anchor=\"start\" x=\"1850\" y=\"-71.7\" font-family=\"Times,serif\" font-size=\"14.00\">guide_ancilla</text>\n",
+ "</g>\n",
+ "<!-- QubitizationQPE_G27 -->\n",
+ "<g id=\"node16\" class=\"node\">\n",
+ "<title>QubitizationQPE_G27</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"2102,-168.5 2102,-186.5 2192,-186.5 2192,-168.5 2102,-168.5\"/>\n",
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+ "<text text-anchor=\"start\" x=\"2123.75\" y=\"-106.2\" font-family=\"Times,serif\" font-size=\"14.00\">ancilla</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G6->QubitizationQPE_G27 -->\n",
+ "<g id=\"edge33\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G6:e->QubitizationQPE_G27:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1955,-145.5C2019.64,-145.5 2036.02,-156.69 2099.34,-156.99\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"2100.5\" cy=\"-157\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"2028.5\" y=\"-158.25\" font-family=\"Times,serif\" font-size=\"10.00\">ceiling(lo ...</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G6->QubitizationQPE_G27 -->\n",
+ "<g id=\"edge35\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G6:e->QubitizationQPE_G27:w</title>\n",
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+ "<text text-anchor=\"middle\" x=\"2028.5\" y=\"-113.25\" font-family=\"Times,serif\" font-size=\"10.00\">N + 1</text>\n",
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+ "<!-- GuidingState_G33 -->\n",
+ "<g id=\"node18\" class=\"node\">\n",
+ "<title>GuidingState_G33</title>\n",
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+ "<text text-anchor=\"start\" x=\"1994.75\" y=\"-75.5\" font-family=\"Times,serif\" font-size=\"10.00\">GuidingState</text>\n",
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+ "<text text-anchor=\"start\" x=\"2013.12\" y=\"-30.7\" font-family=\"Times,serif\" font-size=\"14.00\">junk</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G6->GuidingState_G33 -->\n",
+ "<g id=\"edge31\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G6:e->GuidingState_G33:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1955,-122.5C1986.83,-122.5 1960.88,-62.44 1989.1,-58.68\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"1990.5\" cy=\"-58.59\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"1973.5\" y=\"-99.25\" font-family=\"Times,serif\" font-size=\"10.00\">N</text>\n",
+ "</g>\n",
+ "<!-- ReflectAboutZero_G6->GuidingState_G33 -->\n",
+ "<g id=\"edge32\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G6:e->GuidingState_G33:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1955,-76.5C1978.49,-76.5 1968.43,-38.95 1989.03,-35.72\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"1990.5\" cy=\"-35.61\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"1973.5\" y=\"-61.25\" font-family=\"Times,serif\" font-size=\"10.00\">A</text>\n",
+ "</g>\n",
+ "<!-- QubitizationQPE -->\n",
+ "<g id=\"node11\" class=\"node\">\n",
+ "<title>QubitizationQPE</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"1188,-179.5 1188,-197.5 1278,-197.5 1278,-179.5 1188,-179.5\"/>\n",
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+ "<text text-anchor=\"start\" x=\"1209.75\" y=\"-117.2\" font-family=\"Times,serif\" font-size=\"14.00\">ancilla</text>\n",
+ "</g>\n",
+ "<!-- Adjoint_G15 -->\n",
+ "<g id=\"node13\" class=\"node\">\n",
+ "<title>Adjoint_G15</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"1413,-178.5 1413,-196.5 1597,-196.5 1597,-178.5 1413,-178.5\"/>\n",
+ "<text text-anchor=\"start\" x=\"1415.75\" y=\"-184\" font-family=\"Times,serif\" font-size=\"10.00\">Adjoint(subbloq=QubitizationQPE)</text>\n",
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+ "<text text-anchor=\"start\" x=\"1481.75\" y=\"-116.2\" font-family=\"Times,serif\" font-size=\"14.00\">ancilla</text>\n",
+ "</g>\n",
+ "<!-- QubitizationQPE->Adjoint_G15 -->\n",
+ "<g id=\"edge22\" class=\"edge\">\n",
+ "<title>QubitizationQPE:e->Adjoint_G15:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1278,-168C1337.06,-168 1352.52,-167.03 1410.22,-167\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"1411.5\" cy=\"-167\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"1345.5\" y=\"-170.25\" font-family=\"Times,serif\" font-size=\"10.00\">ceiling(lo ...</text>\n",
+ "</g>\n",
+ "<!-- QubitizationQPE->Adjoint_G15 -->\n",
+ "<g id=\"edge23\" class=\"edge\">\n",
+ "<title>QubitizationQPE:e->Adjoint_G15:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1278,-145C1337.06,-145 1352.52,-144.03 1410.22,-144\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"1411.5\" cy=\"-144\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"1345.5\" y=\"-147.25\" font-family=\"Times,serif\" font-size=\"10.00\">N</text>\n",
+ "</g>\n",
+ "<!-- QubitizationQPE->Adjoint_G15 -->\n",
+ "<g id=\"edge24\" class=\"edge\">\n",
+ "<title>QubitizationQPE:e->Adjoint_G15:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1278,-122C1337.06,-122 1352.52,-121.03 1410.22,-121\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"1411.5\" cy=\"-121\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"1345.5\" y=\"-124.25\" font-family=\"Times,serif\" font-size=\"10.00\">N + 1</text>\n",
+ "</g>\n",
+ "<!-- GuidingState_G12 -->\n",
+ "<g id=\"node12\" class=\"node\">\n",
+ "<title>GuidingState_G12</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"1078,-80 1078,-98 1151,-98 1151,-80 1078,-80\"/>\n",
+ "<text text-anchor=\"start\" x=\"1080.75\" y=\"-85.5\" font-family=\"Times,serif\" font-size=\"10.00\">GuidingState</text>\n",
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+ "<text text-anchor=\"start\" x=\"1099.12\" y=\"-40.7\" font-family=\"Times,serif\" font-size=\"14.00\">junk</text>\n",
+ "</g>\n",
+ "<!-- GuidingState_G12->ReflectAboutZero -->\n",
+ "<g id=\"edge21\" class=\"edge\">\n",
+ "<title>GuidingState_G12:e->ReflectAboutZero:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1151,-45.5C1214.97,-45.5 1230.71,-61.55 1293.37,-61.99\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"1294.5\" cy=\"-61.99\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"1169.5\" y=\"-49.25\" font-family=\"Times,serif\" font-size=\"10.00\">A</text>\n",
+ "</g>\n",
+ "<!-- GuidingState_G12->QubitizationQPE -->\n",
+ "<g id=\"edge19\" class=\"edge\">\n",
+ "<title>GuidingState_G12:e->QubitizationQPE:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1151,-68.5C1169,-68.5 1169.14,-138 1185.47,-144.51\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"1186.53\" cy=\"-144.72\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"1169.5\" y=\"-109.25\" font-family=\"Times,serif\" font-size=\"10.00\">N</text>\n",
+ "</g>\n",
+ "<!-- Adjoint_G15->ReflectAboutZero_G6 -->\n",
+ "<g id=\"edge27\" class=\"edge\">\n",
+ "<title>Adjoint_G15:e->ReflectAboutZero_G6:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1597,-167C1649.82,-167 1779.56,-146.25 1835.09,-145.52\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"1836.5\" cy=\"-145.51\" rx=\"1\" ry=\"1\"/>\n",
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+ "<title>Adjoint_G15:e->ReflectAboutZero_G6:w</title>\n",
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+ "<!-- Adjoint_G15->Adjoint_G46 -->\n",
+ "<g id=\"edge25\" class=\"edge\">\n",
+ "<title>Adjoint_G15:e->Adjoint_G46:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1597,-144C1618.9,-144 1611.83,-111.22 1631.47,-108.66\"/>\n",
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+ "<g id=\"edge13\" class=\"edge\">\n",
+ "<title>Adjoint_G19:e->ReflectAboutZero_G49:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M887,-114.5C904.29,-114.5 905.61,-130.59 921.15,-132.34\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"922.5\" cy=\"-132.42\" rx=\"1\" ry=\"1\"/>\n",
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+ "<g id=\"edge15\" class=\"edge\">\n",
+ "<title>Adjoint_G19:e->ReflectAboutZero_G49:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M887,-91.5C902.56,-91.5 906.88,-87.11 921.03,-86.56\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"922.5\" cy=\"-86.53\" rx=\"1\" ry=\"1\"/>\n",
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+ "<!-- ReflectAboutZero_G22->GuidingState_G0 -->\n",
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+ "<title>ReflectAboutZero_G22:e->GuidingState_G0:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M2869,-111.5C2898.62,-111.5 2876.88,-57.07 2903.29,-53.67\"/>\n",
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+ "<!-- ReflectAboutZero_G22->GuidingState_G0 -->\n",
+ "<g id=\"edge47\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G22:e->GuidingState_G0:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M2869,-65.5C2890.58,-65.5 2884.07,-33.7 2903.01,-30.72\"/>\n",
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+ "<text text-anchor=\"middle\" x=\"2887.5\" y=\"-53.25\" font-family=\"Times,serif\" font-size=\"10.00\">A</text>\n",
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+ "<g id=\"edge48\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G22:e->QubitizationQPE_G54:w</title>\n",
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+ "<!-- ReflectAboutZero_G22->QubitizationQPE_G54 -->\n",
+ "<g id=\"edge50\" class=\"edge\">\n",
+ "<title>ReflectAboutZero_G22:e->QubitizationQPE_G54:w</title>\n",
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+ "<g id=\"node19\" class=\"node\">\n",
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+ "<g id=\"edge37\" class=\"edge\">\n",
+ "<title>QubitizationQPE_G27:e->Adjoint_G36:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M2192,-157C2251.06,-157 2266.52,-156.03 2324.22,-156\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"2325.5\" cy=\"-156\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"2259.5\" y=\"-159.25\" font-family=\"Times,serif\" font-size=\"10.00\">ceiling(lo ...</text>\n",
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+ "<!-- QubitizationQPE_G27->Adjoint_G36 -->\n",
+ "<g id=\"edge38\" class=\"edge\">\n",
+ "<title>QubitizationQPE_G27:e->Adjoint_G36:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M2192,-134C2251.06,-134 2266.52,-133.03 2324.22,-133\"/>\n",
+ "<ellipse fill=\"black\" stroke=\"black\" cx=\"2325.5\" cy=\"-133\" rx=\"1\" ry=\"1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"2259.5\" y=\"-136.25\" font-family=\"Times,serif\" font-size=\"10.00\">N</text>\n",
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+ "<!-- QubitizationQPE_G27->Adjoint_G36 -->\n",
+ "<g id=\"edge39\" class=\"edge\">\n",
+ "<title>QubitizationQPE_G27:e->Adjoint_G36:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M2192,-111C2251.06,-111 2266.52,-110.03 2324.22,-110\"/>\n",
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+ "<title>ReflectAboutZero_G31:e->Adjoint_G3:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M2309,-54C2414.68,-54 2440.93,-74.14 2545.21,-74.5\"/>\n",
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+ "<g id=\"edge34\" class=\"edge\">\n",
+ "<title>GuidingState_G33:e->QubitizationQPE_G27:w</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M2065,-58.5C2082.66,-58.5 2083.3,-125.97 2099.1,-133.35\"/>\n",
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+ "<text text-anchor=\"middle\" x=\"2083.5\" y=\"-99.25\" font-family=\"Times,serif\" font-size=\"10.00\">N</text>\n",
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+ "<g id=\"edge36\" class=\"edge\">\n",
+ "<title>GuidingState_G33:e->ReflectAboutZero_G31:w</title>\n",
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+ "<text text-anchor=\"middle\" x=\"2083.5\" y=\"-40.25\" font-family=\"Times,serif\" font-size=\"10.00\">A</text>\n",
+ "</g>\n",
+ "<!-- Adjoint_G36->Adjoint_G3 -->\n",
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+ "<title>Adjoint_G36:e->Adjoint_G3:w</title>\n",
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+ "<title>Adjoint_G36:e->ReflectAboutZero_G22:w</title>\n",
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+ "<text text-anchor=\"middle\" x=\"2631.5\" y=\"-56.25\" font-family=\"Times,serif\" font-size=\"10.00\">N + 1</text>\n",
+ "</g>\n",
+ "<!-- QubitizationQPE_G40->Adjoint -->\n",
+ "<g id=\"edge7\" class=\"edge\">\n",
+ "<title>QubitizationQPE_G40:e->Adjoint:w</title>\n",
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+ "<title>QubitizationQPE_G40:e->Adjoint:w</title>\n",
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+ "<title>ReflectAboutZero_G44:e->Adjoint_G19:w</title>\n",
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+ "<title>Adjoint_G46:e->ReflectAboutZero_G6:w</title>\n",
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+ "<title>Adjoint_G46:e->ReflectAboutZero_G6:w</title>\n",
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+ "</g>\n",
+ "<!-- ReflectAboutZero_G49->QubitizationQPE -->\n",
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+ "<title>ReflectAboutZero_G49:e->QubitizationQPE:w</title>\n",
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+ "<text text-anchor=\"middle\" x=\"1114.5\" y=\"-169.25\" font-family=\"Times,serif\" font-size=\"10.00\">ceiling(lo ...</text>\n",
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+ "<title>ReflectAboutZero_G49:e->QubitizationQPE:w</title>\n",
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+ "</g>\n",
+ "<!-- walk_ancilla_G61 -->\n",
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+ "<title>walk_ancilla_G61</title>\n",
+ "<text text-anchor=\"middle\" x=\"3206.5\" y=\"-77.33\" font-family=\"Times,serif\" font-size=\"14.00\">walk_ancilla</text>\n",
+ "</g>\n",
+ "<!-- QubitizationQPE_G54->walk_ancilla_G61 -->\n",
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+ "</g>\n",
+ "</g>\n",
+ "</svg>"
+ ],
+ "text/plain": [
+ "<IPython.core.display.SVG object>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "show_bloq(bloq_4_rounds.decompose_bloq().flatten_once())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f131e5ff-4d5b-487b-a84c-56c68a411f71",
+ "metadata": {},
+ "source": [
+ "## Query and gate costs\n",
+ "We will count queries to the above oracles, and arbitrary 1/2-qubit gates as described in the paper."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "id": "cf13f9e4-c65a-41f6-94ef-70168a136191",
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.max_k_xor_sat.shims import generalize_1_2_qubit_gates\n",
+ "\n",
+ "g, sigma = bloq.call_graph(\n",
+ " generalizer=[ignore_alloc_free, ignore_split_join, generalize_1_2_qubit_gates]\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "id": "18fee717-4117-47ce-8929-1aa3e7fba91a",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "#### Counts totals:\n",
+ " - `And`: $\\displaystyle \\left(\\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 1\\right) \\left(4 \\cdot 2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} + N \\left(2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} - 2\\right) + N \\left(2 \\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 2\\right) + N - 4\\right) + \\left(A + 2 N + \\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil\\right) \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + \\left(4 \\cdot 2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} + N \\left(2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} - 2\\right) + N \\left(2 \\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 2\\right) + N - 4\\right) \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil$\n",
+ " - `And†`: $\\displaystyle \\left(\\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 1\\right) \\left(4 \\cdot 2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} + N \\left(2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} - 2\\right) + N \\left(2 \\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 2\\right) + N - 4\\right) + \\left(A + 2 N + \\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil\\right) \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + \\left(4 \\cdot 2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} + N \\left(2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} - 2\\right) + N \\left(2 \\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 2\\right) + N - 4\\right) \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil$\n",
+ " - `ArbitraryGate`: $\\displaystyle 2 \\left(\\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 1\\right) \\left\\lceil{\\operatorname{log}_{2}{\\left(s \\right)}}\\right\\rceil + 2 \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil \\left\\lceil{\\operatorname{log}_{2}{\\left(s \\right)}}\\right\\rceil$\n",
+ " - `ArbitraryGate`: $\\displaystyle \\left(\\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 1\\right) \\left(4 \\cdot 2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} \\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil + G + \\left(2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} - 2\\right) \\left(2 \\left\\lceil{\\operatorname{log}_{2}{\\left(s \\right)}}\\right\\rceil + 3\\right) + \\left(\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 1\\right) \\left\\lfloor{\\frac{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil}{2}}\\right\\rfloor + 13 \\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil + 2 \\left\\lceil{\\operatorname{log}_{2}{\\left(\\left\\lfloor{2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil}}\\right\\rfloor \\right)}}\\right\\rceil + \\left\\lfloor{\\frac{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil}{2}}\\right\\rfloor - 16\\right) + \\left(4 \\cdot 2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} \\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil + G + \\left(2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} - 2\\right) \\left(2 \\left\\lceil{\\operatorname{log}_{2}{\\left(s \\right)}}\\right\\rceil + 3\\right) + \\left(\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 1\\right) \\left\\lfloor{\\frac{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil}{2}}\\right\\rfloor + 13 \\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil + 2 \\left\\lceil{\\operatorname{log}_{2}{\\left(\\left\\lfloor{2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil}}\\right\\rfloor \\right)}}\\right\\rceil + \\left\\lfloor{\\frac{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil}{2}}\\right\\rfloor - 16\\right) \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 2 \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil$\n",
+ " - `C[oracle_O_F]`: $\\displaystyle 2 \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 2$\n",
+ " - `C[oracle_O_F]`: $\\displaystyle 2 \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil$\n",
+ " - `C[oracle_O_H]`: $\\displaystyle 4 \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 2$\n",
+ " - `PrepareIdentity`: $\\displaystyle \\left(\\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 1\\right) \\left(2 \\cdot 2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} + 4 \\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 6\\right) + \\left(2 \\cdot 2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} + 4 \\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 6\\right) \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil$\n",
+ " - `oracle_O_F`: $\\displaystyle \\left(2 \\cdot 2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} - 4\\right) \\left(\\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 1\\right)$\n",
+ " - `oracle_O_F`: $\\displaystyle \\left(2 \\cdot 2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} - 4\\right) \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil$\n",
+ " - `oracle_O_H`: $\\displaystyle \\left(2 \\cdot 2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} - 4\\right) \\left(\\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 1\\right) + \\left(2 \\cdot 2^{\\left\\lceil{\\operatorname{log}_{2}{\\left(\\frac{s \\log{\\left(\\frac{1}{\\gamma^{3}} \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil} - 4\\right) \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil$"
+ ],
+ "text/plain": [
+ "<IPython.core.display.Markdown object>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "show_counts_sigma(sigma)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a6083b59-ed3f-4543-ba28-d7f7b19d2b5a",
+ "metadata": {},
+ "source": [
+ "### Cost from the paper\n",
+ "Theorem 4.9 of the paper states that the algorithm uses:\n",
+ "1. $Q = \\widetilde{O}(s / (\\gamma \\alpha \\lambda))$ queries to oracles for H\n",
+ "2. $\\widetilde{O}(G/\\gamma + \\text{polylog}(Q)/\\gamma + QN)$ gates\n",
+ "\n",
+ "Let us simplify the symbolic costs obtained above and verify if they match."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "id": "9e03abf4-efd3-46b0-83d7-bf3b1b0554a5",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "#### Counts totals:\n",
+ " - `And`: $\\displaystyle \\frac{\\alpha \\lambda \\left(A + 2 N + \\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil\\right) \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + \\left(\\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 1\\right) \\left(- 2 N \\left(\\alpha \\lambda + 3 s \\log{\\left(\\gamma \\right)}\\right) + \\alpha \\lambda \\left(2 N \\left(\\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 1\\right) + N - 4\\right) - 24 s \\log{\\left(\\gamma \\right)}\\right) + \\left(- 2 N \\left(\\alpha \\lambda + 3 s \\log{\\left(\\gamma \\right)}\\right) + \\alpha \\lambda \\left(2 N \\left(\\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 1\\right) + N - 4\\right) - 24 s \\log{\\left(\\gamma \\right)}\\right) \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil}{\\alpha \\lambda}$\n",
+ " - `And†`: $\\displaystyle \\frac{\\alpha \\lambda \\left(A + 2 N + \\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil\\right) \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + \\left(\\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 1\\right) \\left(- 2 N \\left(\\alpha \\lambda + 3 s \\log{\\left(\\gamma \\right)}\\right) + \\alpha \\lambda \\left(2 N \\left(\\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 1\\right) + N - 4\\right) - 24 s \\log{\\left(\\gamma \\right)}\\right) + \\left(- 2 N \\left(\\alpha \\lambda + 3 s \\log{\\left(\\gamma \\right)}\\right) + \\alpha \\lambda \\left(2 N \\left(\\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 1\\right) + N - 4\\right) - 24 s \\log{\\left(\\gamma \\right)}\\right) \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil}{\\alpha \\lambda}$\n",
+ " - `ArbitraryGate`: $\\displaystyle 2 \\cdot \\left(2 \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 1\\right) \\left\\lceil{\\operatorname{log}_{2}{\\left(s \\right)}}\\right\\rceil$\n",
+ " - `ArbitraryGate`: $\\displaystyle \\frac{2 \\alpha \\lambda \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + \\left(\\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 1\\right) \\left(\\alpha \\lambda \\left(G + \\left(\\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 1\\right) \\left\\lfloor{\\frac{\\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil}{2}}\\right\\rfloor + 15 \\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil + \\left\\lfloor{\\frac{\\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil}{2}}\\right\\rfloor - 16\\right) - 24 s \\log{\\left(\\gamma \\right)} \\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 2 \\left(\\alpha \\lambda + 3 s \\log{\\left(\\gamma \\right)}\\right) \\left(2 \\left\\lceil{\\operatorname{log}_{2}{\\left(s \\right)}}\\right\\rceil + 3\\right)\\right) + \\left(\\alpha \\lambda \\left(G + \\left(\\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 1\\right) \\left\\lfloor{\\frac{\\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil}{2}}\\right\\rfloor + 15 \\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil + \\left\\lfloor{\\frac{\\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil}{2}}\\right\\rfloor - 16\\right) - 24 s \\log{\\left(\\gamma \\right)} \\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 2 \\left(\\alpha \\lambda + 3 s \\log{\\left(\\gamma \\right)}\\right) \\left(2 \\left\\lceil{\\operatorname{log}_{2}{\\left(s \\right)}}\\right\\rceil + 3\\right)\\right) \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil}{\\alpha \\lambda}$\n",
+ " - `C[oracle_O_F]`: $\\displaystyle 2 \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 2$\n",
+ " - `C[oracle_O_F]`: $\\displaystyle 2 \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil$\n",
+ " - `C[oracle_O_H]`: $\\displaystyle 4 \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 2$\n",
+ " - `PrepareIdentity`: $\\displaystyle \\frac{2 \\left(\\alpha \\lambda \\left(2 \\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 3\\right) - 6 s \\log{\\left(\\gamma \\right)}\\right) \\left(2 \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 1\\right)}{\\alpha \\lambda}$\n",
+ " - `oracle_O_F`: $\\displaystyle - \\frac{4 \\left(\\alpha \\lambda + 3 s \\log{\\left(\\gamma \\right)}\\right) \\left(\\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil + 1\\right)}{\\alpha \\lambda}$\n",
+ " - `oracle_O_F`: $\\displaystyle \\frac{4 \\left(- \\alpha \\lambda - 3 s \\log{\\left(\\gamma \\right)}\\right) \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil}{\\alpha \\lambda}$\n",
+ " - `oracle_O_H`: $\\displaystyle \\frac{4 \\left(\\alpha \\lambda + 3 s \\log{\\left(\\gamma \\right)}\\right) \\left(- 2 \\left\\lceil{\\frac{1}{\\gamma}}\\right\\rceil - 1\\right)}{\\alpha \\lambda}$"
+ ],
+ "text/plain": [
+ "<IPython.core.display.Markdown object>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "def simplify_2_pow_log(my_expr, inner_term):\n",
+ " # replace `2**(ceil(log2(T)))` upper bound `2T`.\n",
+ " temp = sympy.symbols(f\"_temp\", positive=True, integer=True)\n",
+ " my_expr = my_expr.replace(ceil(log2(inner_term)), temp)\n",
+ " my_expr = my_expr.replace(2**temp, 2 * inner_term)\n",
+ " my_expr = my_expr.replace(temp, ceil(log2(inner_term)))\n",
+ " return my_expr\n",
+ "\n",
+ "def simplify_expression(expr):\n",
+ " if not is_symbolic(expr): return expr\n",
+ " N, A, G, s = sympy.symbols(\"N A G s\", positive=True, integer=True)\n",
+ " lambd, alpha, gamma = sympy.symbols(r\"\\lambda \\alpha \\gamma\", positive=True, real=True)\n",
+ "\n",
+ " expr = simplify_2_pow_log(expr, (s * ln(1/gamma**3)) / (alpha * lambd))\n",
+ " expr = sympy.simplify(expr)\n",
+ " return expr\n",
+ "\n",
+ "sigma_simpl = {k: simplify_expression(v) for k, v in sigma.items()}\n",
+ "show_counts_sigma(sigma_simpl)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2676ae19-41b6-49a9-a16f-706e74b19cf9",
+ "metadata": {},
+ "source": [
+ "### Cost of Phase Estimation\n",
+ "\n",
+ "For simplicity, we can also look at the cost of a single phase estimation call (which is repeated $1/\\gamma$ times to obtain the above algorithm)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "id": "355eab2b-e136-4ff1-b131-a63248bbee31",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "#### Counts totals:\n",
+ " - `And`: $\\displaystyle 2 N \\left\\lceil{\\operatorname{log}_{2}{\\left(- \\log{\\left(\\gamma^{\\frac{3 s}{\\alpha \\lambda}} \\right)} \\right)}}\\right\\rceil - 3 N - 4 - \\frac{\\log{\\left(\\gamma^{24 s} \\gamma^{6 N s} \\right)}}{\\alpha \\lambda}$\n",
+ " - `And†`: $\\displaystyle 2 N \\left\\lceil{\\operatorname{log}_{2}{\\left(- \\log{\\left(\\gamma^{\\frac{3 s}{\\alpha \\lambda}} \\right)} \\right)}}\\right\\rceil - 3 N - 4 - \\frac{\\log{\\left(\\gamma^{24 s} \\gamma^{6 N s} \\right)}}{\\alpha \\lambda}$\n",
+ " - `ArbitraryGate`: $\\displaystyle 2 \\left\\lceil{\\operatorname{log}_{2}{\\left(s \\right)}}\\right\\rceil$\n",
+ " - `ArbitraryGate`: $\\displaystyle G - 4 \\left\\lceil{\\operatorname{log}_{2}{\\left(s \\right)}}\\right\\rceil + \\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil \\left\\lfloor{\\frac{\\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil}{2}}\\right\\rfloor + 15 \\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 22 - \\frac{12 s \\log{\\left(\\gamma \\right)} \\left\\lceil{\\operatorname{log}_{2}{\\left(s \\right)}}\\right\\rceil}{\\alpha \\lambda} - \\frac{24 s \\log{\\left(\\gamma \\right)} \\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil}{\\alpha \\lambda} - \\frac{18 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda}$\n",
+ " - `C[oracle_O_F]`: 2\n",
+ " - `C[oracle_O_H]`: 2\n",
+ " - `PrepareIdentity`: $\\displaystyle 4 \\left\\lceil{\\operatorname{log}_{2}{\\left(- \\frac{3 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda} \\right)}}\\right\\rceil - 6 - \\frac{12 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda}$\n",
+ " - `oracle_O_F`: $\\displaystyle -4 - \\frac{12 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda}$\n",
+ " - `oracle_O_H`: $\\displaystyle -4 - \\frac{12 s \\log{\\left(\\gamma \\right)}}{\\alpha \\lambda}$"
+ ],
+ "text/plain": [
+ "<IPython.core.display.Markdown object>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "g_pe, sigma_pe = bloq.qpe_bloq.call_graph(\n",
+ " generalizer=[ignore_alloc_free, ignore_split_join, generalize_1_2_qubit_gates]\n",
+ ")\n",
+ "sigma_pe = {k: simplify_expression(v) for k, v in sigma_pe.items()}\n",
+ "show_counts_sigma(sigma_pe)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "8cda3ad1-8183-4091-9faf-6c777a283951",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.11.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/walk_operator.py b/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/walk_operator.py
new file mode 100644
index 000000000..48cf3447e
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/walk_operator.py
@@ -0,0 +1,95 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+from functools import cached_property
+
+import attrs
+
+from qualtran import BloqBuilder, Signature, SoquetT
+from qualtran.bloqs.block_encoding import BlockEncoding
+from qualtran.bloqs.reflections.reflection_using_prepare import ReflectionUsingPrepare
+from qualtran.bloqs.state_preparation.black_box_prepare import BlackBoxPrepare
+from qualtran.resource_counting import BloqCountDictT, SympySymbolAllocator
+from qualtran.symbolics import SymbolicFloat, SymbolicInt
+
+
+@attrs.frozen
+class QubitizedWalkOperator(BlockEncoding):
+ r"""Construct a Szegedy Quantum Walk operator of a block encoding.
+
+ Args:
+ block_encoding: The input block-encoding.
+
+ References:
+ [Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity](https://arxiv.org/abs/1805.03662).
+ Babbush et. al. (2018). Figure 1.
+ """
+
+ block_encoding: BlockEncoding
+
+ @property
+ def alpha(self) -> SymbolicFloat:
+ return self.block_encoding.alpha
+
+ @property
+ def system_bitsize(self) -> SymbolicInt:
+ return self.block_encoding.system_bitsize
+
+ @property
+ def ancilla_bitsize(self) -> SymbolicInt:
+ return self.block_encoding.ancilla_bitsize
+
+ @property
+ def resource_bitsize(self) -> SymbolicInt:
+ return self.block_encoding.resource_bitsize
+
+ @property
+ def epsilon(self) -> SymbolicFloat:
+ return self.block_encoding.epsilon
+
+ @property
+ def signal_state(self) -> BlackBoxPrepare:
+ return self.block_encoding.signal_state
+
+ @cached_property
+ def signature(self) -> Signature:
+ return self.block_encoding.signature
+
+ @cached_property
+ def reflect(self) -> ReflectionUsingPrepare:
+ return ReflectionUsingPrepare(self.block_encoding.signal_state, global_phase=-1)
+
+ def build_composite_bloq(self, bb: 'BloqBuilder', **soqs: 'SoquetT') -> dict[str, 'SoquetT']:
+ soqs |= bb.add_d(self.block_encoding, **soqs)
+ soqs |= bb.add_d(
+ self.reflect, **{reg.name: soqs[reg.name] for reg in self.reflect.signature}
+ )
+ return soqs
+
+ def build_call_graph(self, ssa: 'SympySymbolAllocator') -> BloqCountDictT:
+ return {self.block_encoding: 1, self.reflect: 1}
+
+ def __str__(self):
+ return f'Walk[{self.block_encoding}]'
diff --git a/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_list.ipynb b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_list.ipynb
new file mode 100644
index 000000000..efb128a69
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_list.ipynb
@@ -0,0 +1,180 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "3c1703d8",
+ "metadata": {
+ "cq.autogen": "title_cell"
+ },
+ "source": [
+ "# Planted Noisy kXOR: Kikuchi Adjacency List"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "ece15719",
+ "metadata": {
+ "cq.autogen": "top_imports"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran import Bloq, CompositeBloq, BloqBuilder, Signature, Register\n",
+ "from qualtran import QBit, QInt, QUInt, QAny\n",
+ "from qualtran.drawing import show_bloq, show_call_graph, show_counts_sigma\n",
+ "from typing import *\n",
+ "import numpy as np\n",
+ "import sympy\n",
+ "import cirq"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c187b17d",
+ "metadata": {
+ "cq.autogen": "KikuchiNonZeroIndex.bloq_doc.md"
+ },
+ "source": [
+ "## `KikuchiNonZeroIndex`\n",
+ "Adjacency list oracle $O_F$ for the Kikuchi matrix.\n",
+ "\n",
+ "The oracle $O_F$ (Definition 4.5) takes in $i, k$,\n",
+ "and outputs $i, f(i, k)$ where $f(i, k)$ is\n",
+ "index of the $k$-th non-zero entry in row $i$.\n",
+ "\n",
+ "As the Kikuchi matrix is symmetric, we can use the same oracle for both rows and columns.\n",
+ "\n",
+ "The Kikuchi matrix is indexed by $S \\in {[n] \\choose k}$.\n",
+ "For a given row $S$ and column $T$, the entry $\\mathcal{K}_{k}_{S, T}$\n",
+ "is potentially non-zero if $S \\Delta T = U_j$ for some $j$, which is\n",
+ "equivalent to $T = S \\Delta U_j$.\n",
+ "Here, $U_j$ is the $j$-th unique scope in the instance $\\mathcal{I}$.\n",
+ "\n",
+ "To find the $k$-th non-zero entry, we use two oracles:\n",
+ "1. $(S, k) \\mapsto f(S, k)$, implemented by `ColumnOfKthNonZeroEntry`\n",
+ "2. $(S, f(S, k)) \\mapsto k$, implemented by `IndexOfNonZeroColumn`.\n",
+ "\n",
+ "Both these above oracles are unitary: they do not have any entangled ancilla/junk registers.\n",
+ "\n",
+ "\n",
+ "Note on sparsity: This bloq expects the user to provide the sparsity, as it is in general\n",
+ "difficult to compute the precise sparsity of the Kikuchi matrix efficiently. As long as the\n",
+ "provided number is at least the true sparsity, the algorithm will work as expected.\n",
+ "In case the provides sparsity is smaller, it is equivalent to making the remaining entries zero in the final block encoding.\n",
+ "\n",
+ "#### Parameters\n",
+ " - `inst`: the kXOR instance $\\mathcal{I}$.\n",
+ " - `ell`: Kikuchi parameter $\\ell$.\n",
+ " - `s`: sparsity, i.e. max number of non-zero entries in a row/column. \n",
+ "\n",
+ "#### Registers\n",
+ " - `i`: integer in [2^N]\n",
+ " - `k`: integer in [2^N] \n",
+ "\n",
+ "#### References\n",
+ " - [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1). Theorem 4.17, proof para 4 (top of page 39).\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "d329e657",
+ "metadata": {
+ "cq.autogen": "KikuchiNonZeroIndex.bloq_doc.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.optimization.k_xor_sat import KikuchiNonZeroIndex"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8516f446",
+ "metadata": {
+ "cq.autogen": "KikuchiNonZeroIndex.example_instances.md"
+ },
+ "source": [
+ "### Example Instances"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "409ea009",
+ "metadata": {
+ "cq.autogen": "KikuchiNonZeroIndex.kikuchi_nonzero_index"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import example_kxor_instance\n",
+ "\n",
+ "inst = example_kxor_instance()\n",
+ "ell = 8\n",
+ "s = inst.brute_force_sparsity(ell)\n",
+ "\n",
+ "kikuchi_nonzero_index = KikuchiNonZeroIndex(inst, ell, s=s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c08eb466",
+ "metadata": {
+ "cq.autogen": "KikuchiNonZeroIndex.graphical_signature.md"
+ },
+ "source": [
+ "#### Graphical Signature"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "a7478a9a",
+ "metadata": {
+ "cq.autogen": "KikuchiNonZeroIndex.graphical_signature.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.drawing import show_bloqs\n",
+ "show_bloqs([kikuchi_nonzero_index],\n",
+ " ['`kikuchi_nonzero_index`'])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2e07ff5a",
+ "metadata": {
+ "cq.autogen": "KikuchiNonZeroIndex.call_graph.md"
+ },
+ "source": [
+ "### Call Graph"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "138befd7",
+ "metadata": {
+ "cq.autogen": "KikuchiNonZeroIndex.call_graph.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.resource_counting.generalizers import ignore_split_join\n",
+ "kikuchi_nonzero_index_g, kikuchi_nonzero_index_sigma = kikuchi_nonzero_index.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
+ "show_call_graph(kikuchi_nonzero_index_g)\n",
+ "show_counts_sigma(kikuchi_nonzero_index_sigma)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "name": "python"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_list.py b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_list.py
new file mode 100644
index 000000000..8b970e627
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_list.py
@@ -0,0 +1,362 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+from collections import Counter
+
+import numpy as np
+import sympy
+from attrs import frozen
+
+from qualtran import (
+ Bloq,
+ bloq_example,
+ BloqBuilder,
+ BloqDocSpec,
+ QBit,
+ QUInt,
+ Register,
+ Signature,
+ Soquet,
+ SoquetT,
+)
+from qualtran.bloqs.arithmetic import AddK, Equals, Xor
+from qualtran.bloqs.arithmetic.lists import SymmetricDifference
+from qualtran.bloqs.basic_gates import CNOT, ZeroEffect, ZeroState
+from qualtran.bloqs.mcmt import And
+from qualtran.resource_counting import BloqCountDictT, SympySymbolAllocator
+from qualtran.symbolics import SymbolicInt
+
+from .kxor_instance import KXorInstance
+
+
+@frozen
+class ColumnOfKthNonZeroEntry(Bloq):
+ r"""Given $(S, k)$, compute the column of the $k$-th non-zero entry in row $S$.
+
+ If the output is denoted as $f(S, k)$, then this bloq maps
+ $(S, k, z, b)$ to $(S, k, z \oplus f'(S, k), b \oplus (k \ge s))$.
+ where $s$ is the sparsity, and $f'(S, k)$ is by extending $f$
+ such that for all $k \ge s$, $f'(S, k) = k$.
+ Using $f'$ ensures the computation is reversible.
+ Note: we must use the same extension $f'$ for both oracles.
+
+ This algorithm is described by the following pseudo-code:
+ ```
+ def forward(S, k) -> f_S_k:
+ nnz := 0 # counter
+ for j in range(\bar{m}):
+ T := S \Delta U_j
+ if |T| == l:
+ nnz := nnz + 1
+ if nnz == k:
+ f_S_k ^= T
+ ```
+
+ Args:
+ inst: the kXOR instance $\mathcal{I}$.
+ ell: Kikuchi parameter $\ell$.
+
+ Registers:
+ S: index register to store $S \in {[n] \choose \ell}$.
+ k: non-zero entry index register
+ T: index register to store output $T = f(S, k) \in {[n] \choose \ell}$.
+ """
+
+ inst: KXorInstance
+ ell: SymbolicInt
+
+ @property
+ def signature(self) -> 'Signature':
+ return Signature(
+ [
+ Register('S', self.index_dtype, shape=(self.ell,)),
+ Register('k', self.index_dtype, shape=(self.ell,)),
+ Register('T', self.index_dtype, shape=(self.ell,)),
+ Register('flag', QBit()),
+ ]
+ )
+
+ @property
+ def index_dtype(self) -> QUInt:
+ return QUInt(self.inst.index_bitsize)
+
+ def adjoint(self) -> 'ColumnOfKthNonZeroEntry':
+ return self
+
+ def build_call_graph(self, ssa: 'SympySymbolAllocator') -> 'BloqCountDictT':
+ m = self.inst.num_unique_constraints
+ ell, k = self.ell, self.inst.k
+
+ counts_forward = Counter[Bloq]()
+
+ # compute symmetric differences for each constraint
+ counts_forward[SymmetricDifference(ell, k, ell, self.index_dtype)] += m
+
+ # counter
+ counts_forward[AddK(self.index_dtype, 1).controlled()] += m
+
+ # compare counter each time
+ counts_forward[Equals(self.index_dtype)] += m
+
+ # when counter is equal (and updated in this iteration), we can copy the result
+ counts_forward[And()] += m
+ counts_forward[CNOT()] += m # flip the final flag (flipped at most once)
+
+ ### all counts
+ counts = Counter[Bloq]()
+
+ # copy the index (controlled by the final flag)
+ counts[Xor(self.index_dtype).controlled()] += m
+
+ # if nothing matched (final flag = 0), copy k and flip the flag bit
+ counts[Xor(self.index_dtype).controlled()] += 1
+ counts[Xor(QBit())] += 1
+
+ for bloq, nb in counts_forward.items():
+ # compute and uncompute all intermediate values.
+ counts[bloq] += nb
+ counts[bloq.adjoint()] += nb
+
+ return counts
+
+
+@bloq_example
+def _col_kth_nz() -> ColumnOfKthNonZeroEntry:
+ from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import example_kxor_instance
+
+ inst = example_kxor_instance()
+ ell = 8
+
+ col_kth_nz = ColumnOfKthNonZeroEntry(inst, ell)
+ return col_kth_nz
+
+
+@bloq_example
+def _col_kth_nz_symb() -> ColumnOfKthNonZeroEntry:
+ n, m, k, c, s = sympy.symbols("n m k c s", positive=True, integer=True)
+ inst = KXorInstance.symbolic(n=n, m=m, k=k)
+ ell = c * k
+
+ col_kth_nz_symb = ColumnOfKthNonZeroEntry(inst, ell)
+ return col_kth_nz_symb
+
+
+@frozen
+class IndexOfNonZeroColumn(Bloq):
+ r"""Given $(S, T)$, compute $k$ such that $T$ is the $k$-th non-zero entry in row $S$.
+
+ If $f(S, k)$ denotes the $k$-th non-zero entry in row $S$,
+ then this bloq maps $(S, f'(S, k), z, b)$ to $(S, f'(S, k), z \oplus k, b \oplus )$.
+ where $s$ is the sparsity, and $f'(S, k)$ is by extending $f$
+ such that for all $k \ge s$, $f'(S, k) = k$.
+ Using $f'$ ensures the computation is reversible.
+ Note: we must use the same extension $f'$ for both oracles.
+
+ This algorithm is described by the following pseudo-code:
+ ```
+ def reverse(S, f_S_k) -> k:
+ nnz := 0 # counter
+ for j in range(\bar{m}):
+ T := S \Delta U_j
+ if |T| == l:
+ nnz := nnz + 1
+ if T == f_S_k:
+ k ^= nnz
+ ```
+
+ Args:
+ inst: the kXOR instance $\mathcal{I}$.
+ ell: Kikuchi parameter $\ell$.
+
+ Registers:
+ S: index register to store $S \in {[n] \choose \ell}$.
+ k: non-zero entry index register
+ """
+
+ inst: KXorInstance
+ ell: SymbolicInt
+
+ @property
+ def signature(self) -> 'Signature':
+ return Signature(
+ [
+ Register('S', self.index_dtype, shape=(self.ell,)),
+ Register('k', self.index_dtype, shape=(self.ell,)),
+ Register('T', self.index_dtype, shape=(self.ell,)),
+ Register('flag', QBit()),
+ ]
+ )
+
+ @property
+ def index_dtype(self) -> QUInt:
+ return QUInt(self.inst.index_bitsize)
+
+ def adjoint(self) -> 'IndexOfNonZeroColumn':
+ return self
+
+ def build_call_graph(self, ssa: 'SympySymbolAllocator') -> 'BloqCountDictT':
+ m = self.inst.num_unique_constraints
+ ell, k = self.ell, self.inst.k
+
+ counts_forward = Counter[Bloq]()
+
+ # compute symmetric differences for each constraint
+ counts_forward[SymmetricDifference(ell, k, ell, self.index_dtype)] += m
+
+ # counter
+ counts_forward[AddK(self.index_dtype, 1).controlled()] += m
+
+ # compare T to f_S_k each time
+ counts_forward[Equals(self.index_dtype)] += m
+
+ # when T is equal (and counter is updated in this iteration), we can copy the result
+ counts_forward[And()] += m
+ counts_forward[CNOT()] += m # flip the final flag (flipped at most once)
+
+ ### all counts
+ counts = Counter[Bloq]()
+
+ # copy the value of nnz (when final flag = 1)
+ counts[Xor(self.index_dtype).controlled()] += m
+
+ # if nothing matched (final flag = 0), copy k and flip the flag bit
+ counts[Xor(self.index_dtype).controlled()] += 1
+ counts[Xor(QBit())] += 1
+
+ for bloq, nb in counts_forward.items():
+ # compute and uncompute all intermediate values.
+ counts[bloq] += nb
+ counts[bloq.adjoint()] += nb
+
+ return counts
+
+
+@frozen
+class KikuchiNonZeroIndex(Bloq):
+ r"""Adjacency list oracle $O_F$ for the Kikuchi matrix.
+
+ The oracle $O_F$ (Definition 4.5) takes in $i, k$,
+ and outputs $i, f(i, k)$ where $f(i, k)$ is
+ index of the $k$-th non-zero entry in row $i$.
+
+ As the Kikuchi matrix is symmetric, we can use the same oracle for both rows and columns.
+
+ The Kikuchi matrix is indexed by $S \in {[n] \choose k}$.
+ For a given row $S$ and column $T$, the entry $\mathcal{K}_{k}_{S, T}$
+ is potentially non-zero if $S \Delta T = U_j$ for some $j$, which is
+ equivalent to $T = S \Delta U_j$.
+ Here, $U_j$ is the $j$-th unique scope in the instance $\mathcal{I}$.
+
+ To find the $k$-th non-zero entry, we use two oracles:
+ 1. $(S, k) \mapsto f(S, k)$, implemented by `ColumnOfKthNonZeroEntry`
+ 2. $(S, f(S, k)) \mapsto k$, implemented by `IndexOfNonZeroColumn`.
+
+ Both these above oracles are unitary: they do not have any entangled ancilla/junk registers.
+
+
+ Note on sparsity: This bloq expects the user to provide the sparsity, as it is in general
+ difficult to compute the precise sparsity of the Kikuchi matrix efficiently. As long as the
+ provided number is at least the true sparsity, the algorithm will work as expected.
+ In case the provides sparsity is smaller, it is equivalent to making the remaining entries zero in the final block encoding.
+
+ Args:
+ inst: the kXOR instance $\mathcal{I}$.
+ ell: Kikuchi parameter $\ell$.
+ s: sparsity, i.e. max number of non-zero entries in a row/column.
+
+ Registers:
+ i: integer in [2^N]
+ k: integer in [2^N]
+
+ References:
+ [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1)
+ Theorem 4.17, proof para 4 (top of page 39).
+ """
+
+ inst: KXorInstance
+ ell: SymbolicInt
+ s: SymbolicInt
+
+ @property
+ def signature(self) -> 'Signature':
+ return Signature(
+ [
+ Register('S', self.index_dtype, shape=(self.ell,)),
+ Register('k', self.index_dtype, shape=(self.ell,)),
+ ]
+ )
+
+ @property
+ def index_dtype(self) -> QUInt:
+ return QUInt(self.inst.index_bitsize)
+
+ def build_composite_bloq(
+ self, bb: 'BloqBuilder', S: 'Soquet', k: 'Soquet'
+ ) -> dict[str, 'SoquetT']:
+ T = np.array([bb.allocate(dtype=self.index_dtype) for _ in range(int(self.ell))])
+ flag = bb.add(ZeroState())
+ S, k, T, flag = bb.add(
+ ColumnOfKthNonZeroEntry(self.inst, self.ell), S=S, k=k, T=T, flag=flag
+ )
+ S, T, k, flag = bb.add(IndexOfNonZeroColumn(self.inst, self.ell), S=S, T=T, k=k, flag=flag)
+ for soq in k:
+ bb.free(soq)
+ bb.add(ZeroEffect(), q=flag)
+ return dict(S=S, k=T)
+
+ def build_call_graph(self, ssa: 'SympySymbolAllocator') -> 'BloqCountDictT':
+ return {
+ ColumnOfKthNonZeroEntry(self.inst, self.ell): 1,
+ IndexOfNonZeroColumn(self.inst, self.ell): 1,
+ }
+
+
+@bloq_example
+def _kikuchi_nonzero_index() -> KikuchiNonZeroIndex:
+ from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import example_kxor_instance
+
+ inst = example_kxor_instance()
+ ell = 8
+ s = inst.brute_force_sparsity(ell)
+
+ kikuchi_nonzero_index = KikuchiNonZeroIndex(inst, ell, s=s)
+ return kikuchi_nonzero_index
+
+
+@bloq_example
+def _kikuchi_nonzero_index_symb() -> KikuchiNonZeroIndex:
+ from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import KXorInstance
+
+ n, m, k, c, s = sympy.symbols("n m k c s", positive=True, integer=True)
+ inst = KXorInstance.symbolic(n=n, m=m, k=k)
+ ell = c * k
+
+ kikuchi_nonzero_index_symb = KikuchiNonZeroIndex(inst, ell, s=s)
+ return kikuchi_nonzero_index_symb
+
+
+_KIKUCHI_NONZERO_INDEX_DOC = BloqDocSpec(
+ bloq_cls=KikuchiNonZeroIndex, examples=[_kikuchi_nonzero_index]
+)
diff --git a/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_list_test.py b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_list_test.py
new file mode 100644
index 000000000..fd6875bdf
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_list_test.py
@@ -0,0 +1,78 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+from unittest.mock import ANY
+
+import pytest
+import sympy
+
+import qualtran.testing as qlt_testing
+from qualtran.resource_counting import big_O, GateCounts, get_cost_value, QECGatesCost
+from qualtran.symbolics import ceil, log2
+
+from .kikuchi_adjacency_list import (
+ _col_kth_nz,
+ _col_kth_nz_symb,
+ _kikuchi_nonzero_index,
+ _kikuchi_nonzero_index_symb,
+)
+
+
+@pytest.mark.parametrize(
+ "bloq_ex",
+ [_col_kth_nz, _col_kth_nz_symb, _kikuchi_nonzero_index, _kikuchi_nonzero_index_symb],
+ ids=lambda bloq_ex: bloq_ex.name,
+)
+def test_examples(bloq_autotester, bloq_ex):
+ if bloq_autotester.check_name == 'serialize':
+ pytest.skip()
+
+ bloq_autotester(bloq_ex)
+
+
+def test_cost_col_kth_nz():
+ n, m, k, c, s = sympy.symbols("n m k c s", positive=True, integer=True)
+ l = c * k
+ logn = ceil(log2(n))
+ logl = ceil(log2(l))
+
+ bloq = _col_kth_nz_symb()
+ cost = get_cost_value(bloq, QECGatesCost())
+ assert cost == GateCounts(
+ toffoli=(m + 1) * logn,
+ cswap=4 * l * m * (logl + 1) * logn,
+ and_bloq=(
+ 4 * m * (logn - 1)
+ + (
+ 2
+ * m
+ * (
+ 2 * l * ((2 * logn + 1) * (logl + 1))
+ + l
+ + k
+ + 2 * ((logn - 1) * (l + k - 1))
+ + 2 * ceil(log2(l + k))
+ - 4
+ )
+ )
+ + m
+ ),
+ clifford=ANY,
+ measurement=ANY,
+ )
+ assert big_O(cost.total_t_count()) == big_O(l * m * logn * logl)
+
+
+@pytest.mark.notebook
+def test_notebook():
+ qlt_testing.execute_notebook('kikuchi_adjacency_list')
diff --git a/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_matrix.ipynb b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_matrix.ipynb
new file mode 100644
index 000000000..599e88a21
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_matrix.ipynb
@@ -0,0 +1,197 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "f82c4ce3",
+ "metadata": {
+ "cq.autogen": "title_cell"
+ },
+ "source": [
+ "# Planted Noisy kXOR: Kikuchi Adjacency Matrix"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "8910a435",
+ "metadata": {
+ "cq.autogen": "top_imports"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran import Bloq, CompositeBloq, BloqBuilder, Signature, Register\n",
+ "from qualtran import QBit, QInt, QUInt, QAny\n",
+ "from qualtran.drawing import show_bloq, show_call_graph, show_counts_sigma\n",
+ "from typing import *\n",
+ "import numpy as np\n",
+ "import sympy\n",
+ "import cirq"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3702603c",
+ "metadata": {
+ "cq.autogen": "KikuchiMatrixEntry.bloq_doc.md"
+ },
+ "source": [
+ "## `KikuchiMatrixEntry`\n",
+ "Adjacency matrix oracle for the Kikuchi matrix.\n",
+ "\n",
+ "Given a kXOR instance $\\mathcal{I}$ with $n$ variables, $m$ constraints,\n",
+ "the Kikuchi matrix with parameter $\\ell$ is indexed by ${[n] \\choose l}$.\n",
+ "For $S, T \\in {[n] \\choose l}$, the entry is given by\n",
+ "$H_{S, T} = B_{\\mathcal{I}}(S \\Delta T)/M$, where $M$ is the max entry.\n",
+ "\n",
+ "This bloq implements the transform:\n",
+ " $$\n",
+ " |0 \\rangle |S\\rangle |T\\rangle\n",
+ " \\mapsto\n",
+ " (\\sqrt{H_{S, T}}|0\\rangle + \\sqrt{1 - |H_{S, T}|}|1\\rangle)|S\\rangle |T\\rangle\n",
+ " $$\n",
+ "\n",
+ "This is equivalent to $O_H$ (Def. 4.3) from the paper, but is optimized to classically\n",
+ "compute the `arccos` of the entries, and directly apply the rotation,\n",
+ "instead of computing them using a quantum circuit.\n",
+ "\n",
+ "This bloq performs the following steps\n",
+ "1. Compute the symmetric difference $D = S \\Delta T$.\n",
+ "2. Compute the index $j$ s.t. $U_j = D$ (where $U_j$ are a list of unique scopes)\n",
+ "4. Apply a controlled Y-rotation with angle for the $j$-th entry.\n",
+ "5. Uncompute steps 3, 2, 1.\n",
+ "\n",
+ "#### Parameters\n",
+ " - `inst`: k-XOR instance\n",
+ " - `ell`: the Kikuchi parameter $\\ell$, must be a multiple of $k$.\n",
+ " - `entry_bitsize`: number of bits to approximate each rotation angle to.\n",
+ " - `cv`: single bit control value (0 or 1), or None for uncontrolled (default). \n",
+ "\n",
+ "#### Registers\n",
+ " - `S`: row index\n",
+ " - `T`: column index\n",
+ " - `q`: the qubit to rotate by $Ry(2 \\arccos(\\sqrt{H_{S,T} / M}))$ as defined above. \n",
+ "\n",
+ "#### References\n",
+ " - [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1). Definition 4.3. Theorem 4.17 para 3.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "06c85c6c",
+ "metadata": {
+ "cq.autogen": "KikuchiMatrixEntry.bloq_doc.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.optimization.k_xor_sat import KikuchiMatrixEntry"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f45d82af",
+ "metadata": {
+ "cq.autogen": "KikuchiMatrixEntry.example_instances.md"
+ },
+ "source": [
+ "### Example Instances"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "e5a5035e",
+ "metadata": {
+ "cq.autogen": "KikuchiMatrixEntry.kikuchi_matrix_entry_symb"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import KXorInstance\n",
+ "\n",
+ "n, m, k, c = sympy.symbols(\"n m k c\", positive=True, integer=True)\n",
+ "inst = KXorInstance.symbolic(n=n, m=m, k=k)\n",
+ "ell = c * k\n",
+ "\n",
+ "kikuchi_matrix_entry_symb = KikuchiMatrixEntry(inst, ell, entry_bitsize=3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "802ff581",
+ "metadata": {
+ "cq.autogen": "KikuchiMatrixEntry.kikuchi_matrix_entry"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import example_kxor_instance\n",
+ "\n",
+ "inst = example_kxor_instance()\n",
+ "ell = 8\n",
+ "\n",
+ "kikuchi_matrix_entry = KikuchiMatrixEntry(inst, ell, entry_bitsize=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "fd2fd175",
+ "metadata": {
+ "cq.autogen": "KikuchiMatrixEntry.graphical_signature.md"
+ },
+ "source": [
+ "#### Graphical Signature"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5d9b2e3a",
+ "metadata": {
+ "cq.autogen": "KikuchiMatrixEntry.graphical_signature.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.drawing import show_bloqs\n",
+ "show_bloqs([kikuchi_matrix_entry_symb, kikuchi_matrix_entry],\n",
+ " ['`kikuchi_matrix_entry_symb`', '`kikuchi_matrix_entry`'])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "649be2c9",
+ "metadata": {
+ "cq.autogen": "KikuchiMatrixEntry.call_graph.md"
+ },
+ "source": [
+ "### Call Graph"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "a901dca4",
+ "metadata": {
+ "cq.autogen": "KikuchiMatrixEntry.call_graph.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.resource_counting.generalizers import ignore_split_join\n",
+ "kikuchi_matrix_entry_symb_g, kikuchi_matrix_entry_symb_sigma = kikuchi_matrix_entry_symb.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
+ "show_call_graph(kikuchi_matrix_entry_symb_g)\n",
+ "show_counts_sigma(kikuchi_matrix_entry_symb_sigma)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "name": "python"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_matrix.py b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_matrix.py
new file mode 100644
index 000000000..c198e7800
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_matrix.py
@@ -0,0 +1,184 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+from collections import Counter
+from functools import cached_property
+
+import attrs
+import sympy
+from attrs import frozen
+
+from qualtran import (
+ AddControlledT,
+ Bloq,
+ bloq_example,
+ BloqDocSpec,
+ CtrlSpec,
+ QAny,
+ QBit,
+ QFxp,
+ QUInt,
+ Signature,
+)
+from qualtran.bloqs.arithmetic.lists import SymmetricDifference
+from qualtran.resource_counting import BloqCountDictT, SympySymbolAllocator
+from qualtran.symbolics import SymbolicInt
+
+from .kxor_instance import KXorInstance
+from .load_kxor_instance import LoadUniqueScopeIndex, PRGAUniqueConstraintRHS
+
+
+@frozen
+class KikuchiMatrixEntry(Bloq):
+ r"""Adjacency matrix oracle for the Kikuchi matrix.
+
+ Given a kXOR instance $\mathcal{I}$ with $n$ variables, $m$ constraints,
+ the Kikuchi matrix with parameter $\ell$ is indexed by ${[n] \choose l}$.
+ For $S, T \in {[n] \choose l}$, the entry is given by
+ $H_{S, T} = B_{\mathcal{I}}(S \Delta T)/M$, where $M$ is the max entry.
+
+ This bloq implements the transform:
+ $$
+ |0 \rangle |S\rangle |T\rangle
+ \mapsto
+ (\sqrt{H_{S, T}}|0\rangle + \sqrt{1 - |H_{S, T}|}|1\rangle)|S\rangle |T\rangle
+ $$
+
+ This is equivalent to $O_H$ (Def. 4.3) from the paper, but is optimized to classically
+ compute the `arccos` of the entries, and directly apply the rotation,
+ instead of computing them using a quantum circuit.
+
+ This bloq performs the following steps
+ 1. Compute the symmetric difference $D = S \Delta T$.
+ 2. Compute the index $j$ s.t. $U_j = D$ (where $U_j$ are a list of unique scopes)
+ 4. Apply a controlled Y-rotation with angle for the $j$-th entry.
+ 5. Uncompute steps 3, 2, 1.
+
+ Args:
+ inst: k-XOR instance
+ ell: the Kikuchi parameter $\ell$, must be a multiple of $k$.
+ entry_bitsize: number of bits to approximate each rotation angle to.
+ cv: single bit control value (0 or 1), or None for uncontrolled (default).
+
+ Registers:
+ S: row index
+ T: column index
+ q: the qubit to rotate by $Ry(2 \arccos(\sqrt{H_{S,T} / M}))$ as defined above.
+
+ References:
+ [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1)
+ Definition 4.3. Theorem 4.17 para 3.
+ """
+
+ inst: KXorInstance
+ ell: SymbolicInt
+ entry_bitsize: SymbolicInt
+ is_controlled: bool = False
+
+ @property
+ def signature(self) -> 'Signature':
+ return Signature.build_from_dtypes(
+ ctrl=QAny(1 if self.is_controlled else 0),
+ S=QAny(self.composite_index_bitsize),
+ T=QAny(self.composite_index_bitsize),
+ q=QBit(),
+ )
+
+ @cached_property
+ def index_dtype(self) -> QUInt:
+ return QUInt(self.inst.index_bitsize)
+
+ @cached_property
+ def composite_index_bitsize(self) -> SymbolicInt:
+ """total number of bits to store `l` indices in `[n]`."""
+ return self.ell * self.inst.index_bitsize
+
+ @cached_property
+ def rotation_angle_dtype(self):
+ return QFxp(self.entry_bitsize, self.entry_bitsize)
+
+ def build_call_graph(self, ssa: 'SympySymbolAllocator') -> BloqCountDictT:
+ counts = Counter[Bloq]()
+
+ # S \Delta T
+ symm_diff = SymmetricDifference(self.ell, self.ell, self.inst.k, self.index_dtype)
+ counts[symm_diff] += 1
+ counts[symm_diff.adjoint()] += 1
+
+ # Map S to j, such that U_j = S
+ load_idx = LoadUniqueScopeIndex(self.inst)
+ counts[load_idx] += 1
+ counts[load_idx.adjoint()] += 1
+
+ # apply the rotation
+ rotation: Bloq = PRGAUniqueConstraintRHS(self.inst, self.entry_bitsize)
+ if self.is_controlled:
+ rotation = rotation.controlled()
+ counts[rotation] += 1
+
+ return counts
+
+ def get_ctrl_system(self, ctrl_spec: 'CtrlSpec') -> tuple['Bloq', 'AddControlledT']:
+ from qualtran.bloqs.mcmt.specialized_ctrl import get_ctrl_system_1bit_cv_from_bloqs
+
+ ctrl_bit, ctrl_bloq = (
+ (1, self) if self.is_controlled else (None, attrs.evolve(self, is_controlled=True))
+ )
+
+ return get_ctrl_system_1bit_cv_from_bloqs(
+ self,
+ ctrl_spec,
+ current_ctrl_bit=ctrl_bit,
+ bloq_with_ctrl=ctrl_bloq,
+ ctrl_reg_name='ctrl',
+ )
+
+
+@bloq_example
+def _kikuchi_matrix_entry() -> KikuchiMatrixEntry:
+ from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import example_kxor_instance
+
+ inst = example_kxor_instance()
+ ell = 8
+
+ kikuchi_matrix_entry = KikuchiMatrixEntry(inst, ell, entry_bitsize=3)
+ return kikuchi_matrix_entry
+
+
+@bloq_example
+def _kikuchi_matrix_entry_symb() -> KikuchiMatrixEntry:
+ from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import KXorInstance
+
+ n, m, k, c = sympy.symbols("n m k c", positive=True, integer=True)
+ inst = KXorInstance.symbolic(n=n, m=m, k=k)
+ ell = c * k
+
+ kikuchi_matrix_entry_symb = KikuchiMatrixEntry(inst, ell, entry_bitsize=3)
+ return kikuchi_matrix_entry_symb
+
+
+_KIKUCHI_MATRIX_ENTRY_DOC = BloqDocSpec(
+ bloq_cls=KikuchiMatrixEntry, examples=[_kikuchi_matrix_entry_symb, _kikuchi_matrix_entry]
+)
diff --git a/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_matrix_test.py b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_matrix_test.py
new file mode 100644
index 000000000..6159296be
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_matrix_test.py
@@ -0,0 +1,93 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+from unittest.mock import ANY
+
+import pytest
+import sympy
+from attrs import evolve
+
+import qualtran.testing as qlt_testing
+from qualtran.resource_counting import big_O, GateCounts, get_cost_value, QECGatesCost
+from qualtran.symbolics import ceil, log2
+
+from .kikuchi_adjacency_matrix import _kikuchi_matrix_entry, _kikuchi_matrix_entry_symb
+
+
+@pytest.mark.parametrize("bloq_ex", [_kikuchi_matrix_entry, _kikuchi_matrix_entry_symb])
+def test_examples(bloq_autotester, bloq_ex):
+ if bloq_autotester.check_name == 'serialize':
+ pytest.skip()
+
+ bloq_autotester(bloq_ex)
+
+
+def test_controlled_cost():
+ bloq = _kikuchi_matrix_entry()
+ _, sigma = bloq.call_graph(max_depth=2)
+ _, ctrl_sigma = bloq.controlled().call_graph(max_depth=2)
+
+ # should only differ in QROM call for loading absolute amplitudes
+ a_minus_b = set(sigma.items()) - set(ctrl_sigma.items())
+ b_minus_a = set(ctrl_sigma.items()) - set(sigma.items())
+ assert len(a_minus_b) == 1
+ assert len(b_minus_a) == 1
+
+ ((qrom, na),) = a_minus_b
+ ((ctrl_qrom, nb),) = b_minus_a
+ assert na == nb
+ assert evolve(qrom, num_controls=1) == ctrl_qrom # type: ignore
+
+
+def test_cost():
+ bloq = _kikuchi_matrix_entry()
+
+ gc = get_cost_value(bloq, QECGatesCost())
+ assert gc == GateCounts(
+ cswap=512, and_bloq=1301, clifford=12518, measurement=1301, rotation=ANY
+ )
+
+
+def test_cost_symb():
+ bloq = _kikuchi_matrix_entry_symb()
+ n, m, k, c = sympy.symbols("n m k c", positive=True, integer=True)
+
+ l = c * k
+ logl = ceil(log2(l))
+ logn = ceil(log2(n))
+ logm = ceil(log2(m))
+
+ gc = get_cost_value(bloq, QECGatesCost())
+ assert gc == GateCounts(
+ cswap=4 * l * (logl + 1) * logn,
+ and_bloq=(
+ 4 * l * ((2 * logn + 1) * (logl + 1))
+ + 4 * l
+ + 2 * m * (k * logn - 1)
+ + 2 * m
+ + 4 * ((2 * l - 1) * (logn - 1))
+ + logm
+ + 4 * ceil(log2(2 * l))
+ - 10
+ ),
+ rotation=ANY,
+ clifford=ANY,
+ measurement=ANY,
+ )
+
+ assert big_O(gc.total_t_count()) == big_O(l * logn * logl + k * m * logn)
+
+
+@pytest.mark.notebook
+def test_notebook():
+ qlt_testing.execute_notebook('kikuchi_adjacency_matrix')
diff --git a/qualtran/bloqs/optimization/k_xor_sat/kikuchi_block_encoding.ipynb b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_block_encoding.ipynb
new file mode 100644
index 000000000..f230ac0ab
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_block_encoding.ipynb
@@ -0,0 +1,183 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "e1597556",
+ "metadata": {
+ "cq.autogen": "title_cell"
+ },
+ "source": [
+ "# Noisy kXOR: Block-encoding the Kikuchi Matrix\n",
+ "\n",
+ "Section 4.4.2 Simulating the Kikuchi Hamiltonian\n",
+ "\n",
+ "This module contains oracles to implement the block-encoding of the Kikuchi\n",
+ "Hamiltonian corresponding to an input k-XOR-SAT instance.\n",
+ "\n",
+ "References:\n",
+ " [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1)\n",
+ " Section 4.4.2 for algorithm. Section 2.4 for definitions and notation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "8d69b0bd",
+ "metadata": {
+ "cq.autogen": "top_imports"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran import Bloq, CompositeBloq, BloqBuilder, Signature, Register\n",
+ "from qualtran import QBit, QInt, QUInt, QAny\n",
+ "from qualtran.drawing import show_bloq, show_call_graph, show_counts_sigma\n",
+ "from typing import *\n",
+ "import numpy as np\n",
+ "import sympy\n",
+ "import cirq"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4e549ab8",
+ "metadata": {
+ "cq.autogen": "KikuchiHamiltonian.bloq_doc.md"
+ },
+ "source": [
+ "## `KikuchiHamiltonian`\n",
+ "Block encoding of the Kikuchi matrix $\\mathcal{K}_\\ell$.\n",
+ "\n",
+ "This is implemented by a sparse matrix block encoding using the adjacency matrix\n",
+ "and adjacency list oracles.\n",
+ "\n",
+ "This assumes a default sparsity of $\\bar{m}$, which is the number of unique\n",
+ "scopes in the instance $\\mathcal{I}$.\n",
+ "If a better bound on sparsity is known, it can be passed in by the user.\n",
+ "\n",
+ "#### Parameters\n",
+ " - `inst`: kXOR instance $\\mathcal{I}$.\n",
+ " - `ell`: Kikuchi parameter $\\ell$.\n",
+ " - `entry_bitsize`: Number of bits $b$ to approximate the matrix entries (angles) to.\n",
+ " - `s`: sparsity of the Kikuchi matrix, defaults to $\\bar{m}$.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "9a89ce06",
+ "metadata": {
+ "cq.autogen": "KikuchiHamiltonian.bloq_doc.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.optimization.k_xor_sat import KikuchiHamiltonian"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9b0195ad",
+ "metadata": {
+ "cq.autogen": "KikuchiHamiltonian.example_instances.md"
+ },
+ "source": [
+ "### Example Instances"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "8660eb37",
+ "metadata": {
+ "cq.autogen": "KikuchiHamiltonian.kikuchi_matrix"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import example_kxor_instance\n",
+ "\n",
+ "inst = example_kxor_instance()\n",
+ "ell = 8\n",
+ "\n",
+ "kikuchi_matrix = KikuchiHamiltonian(inst, ell)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "4f6f324e",
+ "metadata": {
+ "cq.autogen": "KikuchiHamiltonian.kikuchi_matrix_symb"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import KXorInstance\n",
+ "\n",
+ "n, m, k, c = sympy.symbols(\"n m k c\", positive=True, integer=True)\n",
+ "inst = KXorInstance.symbolic(n=n, m=m, k=k)\n",
+ "ell = c * k\n",
+ "\n",
+ "kikuchi_matrix_symb = KikuchiHamiltonian(inst, ell)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "312f1765",
+ "metadata": {
+ "cq.autogen": "KikuchiHamiltonian.graphical_signature.md"
+ },
+ "source": [
+ "#### Graphical Signature"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "1419c085",
+ "metadata": {
+ "cq.autogen": "KikuchiHamiltonian.graphical_signature.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.drawing import show_bloqs\n",
+ "show_bloqs([kikuchi_matrix, kikuchi_matrix_symb],\n",
+ " ['`kikuchi_matrix`', '`kikuchi_matrix_symb`'])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "720f08a4",
+ "metadata": {
+ "cq.autogen": "KikuchiHamiltonian.call_graph.md"
+ },
+ "source": [
+ "### Call Graph"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "c492110d",
+ "metadata": {
+ "cq.autogen": "KikuchiHamiltonian.call_graph.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.resource_counting.generalizers import ignore_split_join\n",
+ "kikuchi_matrix_g, kikuchi_matrix_sigma = kikuchi_matrix.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
+ "show_call_graph(kikuchi_matrix_g)\n",
+ "show_counts_sigma(kikuchi_matrix_sigma)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "name": "python"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/qualtran/bloqs/optimization/k_xor_sat/kikuchi_block_encoding.py b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_block_encoding.py
new file mode 100644
index 000000000..3862563fb
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_block_encoding.py
@@ -0,0 +1,236 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+"""Section 4.4.2 Simulating the Kikuchi Hamiltonian
+
+This module contains oracles to implement the block-encoding of the Kikuchi
+Hamiltonian corresponding to an input k-XOR-SAT instance.
+
+References:
+ [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1)
+ Section 4.4.2 for algorithm. Section 2.4 for definitions and notation.
+"""
+from functools import cached_property
+
+import sympy
+from attrs import field, frozen
+
+from qualtran import (
+ bloq_example,
+ BloqBuilder,
+ BloqDocSpec,
+ BQUInt,
+ QAny,
+ QBit,
+ QUInt,
+ Signature,
+ Soquet,
+ SoquetT,
+)
+from qualtran.bloqs.block_encoding import BlockEncoding
+from qualtran.bloqs.block_encoding.sparse_matrix import RowColumnOracle
+from qualtran.bloqs.block_encoding.sparse_matrix_hermitian import (
+ SparseMatrixHermitian,
+ SqrtEntryOracle,
+)
+from qualtran.bloqs.state_preparation.black_box_prepare import BlackBoxPrepare
+from qualtran.resource_counting import BloqCountDictT, SympySymbolAllocator
+from qualtran.symbolics import is_symbolic, SymbolicFloat, SymbolicInt
+
+from .kikuchi_adjacency_list import KikuchiNonZeroIndex
+from .kikuchi_adjacency_matrix import KikuchiMatrixEntry
+from .kxor_instance import KXorInstance
+
+
+@frozen
+class BlackBoxKikuchiEntryOracle(SqrtEntryOracle):
+ r"""Wrapper around the adjacency matrix oracle $O_H$ of the Kikuchi graph."""
+
+ O_H: KikuchiMatrixEntry
+
+ @cached_property
+ def signature(self) -> Signature:
+ return Signature.build_from_dtypes(
+ q=QBit(), i=QAny(self.system_bitsize), j=QAny(self.system_bitsize)
+ )
+
+ @property
+ def system_bitsize(self) -> SymbolicInt:
+ return self.O_H.composite_index_bitsize
+
+ @property
+ def epsilon(self) -> SymbolicFloat:
+ """precision due to fixed-point approximation of entries.
+
+ In the good case, whp (i.e. 1 - o(1)), the entries are in [-2, 2],
+ whose corresponding angles can be represented exactly with 3 bits.
+ I.e. `arccos(sqrt(x / 2)) / pi` for `x in [-2, 2]` are `2, 1.5, 1, 0.5, 0`.
+ """
+ return 0
+
+ @property
+ def _phasegrad_bitsize(self) -> SymbolicInt:
+ return self.O_H.entry_bitsize
+
+ def build_composite_bloq(
+ self, bb: 'BloqBuilder', q: 'Soquet', i: 'Soquet', j: 'Soquet'
+ ) -> dict[str, 'SoquetT']:
+ i, j, q = bb.add(self.O_H, S=i, T=j, q=q)
+ return dict(q=q, i=i, j=j)
+
+
+@frozen
+class BlackBoxKikuchiRowColumnOracle(RowColumnOracle):
+ r"""Wrapper around the adjacency list oracle $O_F$ of the Kikuchi graph."""
+
+ O_F: KikuchiNonZeroIndex
+
+ @cached_property
+ def signature(self) -> Signature:
+ return Signature.build_from_dtypes(
+ l=BQUInt(self.system_bitsize, self.num_nonzero), i=QUInt(self.system_bitsize)
+ )
+
+ @property
+ def system_bitsize(self) -> SymbolicInt:
+ return self.O_F.index_dtype.num_qubits * self.O_F.ell
+
+ @property
+ def num_nonzero(self) -> SymbolicInt:
+ return self.O_F.s
+
+ def build_composite_bloq(
+ self, bb: 'BloqBuilder', l: 'Soquet', i: 'Soquet'
+ ) -> dict[str, 'SoquetT']:
+ i, l = bb.add(self.O_F, S=i, k=l)
+ return dict(l=l, i=i)
+
+ def build_call_graph(self, ssa: 'SympySymbolAllocator') -> 'BloqCountDictT':
+ return {self.O_F: 1}
+
+
+@frozen
+class KikuchiHamiltonian(BlockEncoding):
+ r"""Block encoding of the Kikuchi matrix $\mathcal{K}_\ell$.
+
+ This is implemented by a sparse matrix block encoding using the adjacency matrix
+ and adjacency list oracles.
+
+ This assumes a default sparsity of $\bar{m}$, which is the number of unique
+ scopes in the instance $\mathcal{I}$.
+ If a better bound on sparsity is known, it can be passed in by the user.
+
+ Args:
+ inst: kXOR instance $\mathcal{I}$.
+ ell: Kikuchi parameter $\ell$.
+ entry_bitsize: Number of bits $b$ to approximate the matrix entries (angles) to.
+ s: sparsity of the Kikuchi matrix, defaults to $\bar{m}$.
+ """
+
+ inst: KXorInstance
+ ell: SymbolicInt
+ entry_bitsize: SymbolicInt = field()
+ s: SymbolicInt = field()
+
+ @s.default
+ def _default_sparsity(self) -> SymbolicInt:
+ return self.inst.num_unique_constraints
+
+ @entry_bitsize.default
+ def _default_entry_bitsize(self):
+ if is_symbolic(self.inst.max_rhs) or self.inst.max_rhs == 2:
+ # one T gate suffices!
+ return 3
+ raise ValueError("Entries outside range [-2, 2], please specify an explicit entry_bitsize.")
+
+ @cached_property
+ def signature(self) -> 'Signature':
+ return Signature.build(
+ system=self.system_bitsize, ancilla=self.ancilla_bitsize, resource=self.resource_bitsize
+ )
+
+ @cached_property
+ def _sparse_matrix_encoding(self) -> SparseMatrixHermitian:
+ blackbox_O_F = BlackBoxKikuchiRowColumnOracle(self.oracle_O_F)
+ blackbox_O_H = BlackBoxKikuchiEntryOracle(self.oracle_O_H)
+ return SparseMatrixHermitian(
+ col_oracle=blackbox_O_F, entry_oracle=blackbox_O_H, eps=blackbox_O_H.epsilon
+ )
+
+ @cached_property
+ def oracle_O_H(self) -> KikuchiMatrixEntry:
+ r"""Maps $|i, j\rangle |0\rangle$ to $|i, j\rangle (\sqrt{A_{ij}} |0\rangle + \sqrt{1 - |A_{ij}|} |1\rangle)"""
+ return KikuchiMatrixEntry(inst=self.inst, ell=self.ell, entry_bitsize=self.entry_bitsize)
+
+ @cached_property
+ def oracle_O_F(self) -> KikuchiNonZeroIndex:
+ r"""Maps `i, k` to `i, f(i, k)` where `f(i, k)` is the column of the `k`-th nonzero entry in row `i`."""
+ return KikuchiNonZeroIndex(inst=self.inst, ell=self.ell, s=self.s)
+
+ @property
+ def alpha(self) -> SymbolicFloat:
+ return self._sparse_matrix_encoding.alpha
+
+ @property
+ def system_bitsize(self) -> SymbolicInt:
+ return self._sparse_matrix_encoding.system_bitsize
+
+ @property
+ def ancilla_bitsize(self) -> SymbolicInt:
+ return self._sparse_matrix_encoding.ancilla_bitsize
+
+ @property
+ def resource_bitsize(self) -> SymbolicInt:
+ return self._sparse_matrix_encoding.resource_bitsize
+
+ @property
+ def epsilon(self) -> SymbolicFloat:
+ return self._sparse_matrix_encoding.epsilon
+
+ @property
+ def signal_state(self) -> BlackBoxPrepare:
+ return self._sparse_matrix_encoding.signal_state
+
+ def build_composite_bloq(self, bb: 'BloqBuilder', **soqs: 'SoquetT') -> dict[str, 'SoquetT']:
+ return bb.add_d(self._sparse_matrix_encoding, **soqs)
+
+ def __str__(self):
+ return 'B[K_l]'
+
+
+@bloq_example
+def _kikuchi_matrix() -> KikuchiHamiltonian:
+ from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import example_kxor_instance
+
+ inst = example_kxor_instance()
+ ell = 8
+
+ kikuchi_matrix = KikuchiHamiltonian(inst, ell)
+ return kikuchi_matrix
+
+
+@bloq_example
+def _kikuchi_matrix_symb() -> KikuchiHamiltonian:
+ from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import KXorInstance
+
+ n, m, k, c = sympy.symbols("n m k c", positive=True, integer=True)
+ inst = KXorInstance.symbolic(n=n, m=m, k=k)
+ ell = c * k
+
+ kikuchi_matrix_symb = KikuchiHamiltonian(inst, ell)
+ return kikuchi_matrix_symb
+
+
+_KIKUCHI_HAMILTONIAN_DOC = BloqDocSpec(
+ bloq_cls=KikuchiHamiltonian, examples=[_kikuchi_matrix, _kikuchi_matrix_symb]
+)
diff --git a/qualtran/bloqs/optimization/k_xor_sat/kikuchi_block_encoding_test.py b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_block_encoding_test.py
new file mode 100644
index 000000000..ad8ef0951
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/kikuchi_block_encoding_test.py
@@ -0,0 +1,58 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+import pytest
+
+import qualtran.testing as qlt_testing
+from qualtran.bloqs.basic_gates import Swap
+from qualtran.resource_counting import get_cost_value, QECGatesCost
+
+from .kikuchi_block_encoding import _kikuchi_matrix, _kikuchi_matrix_symb
+
+
+@pytest.mark.parametrize("bloq_ex", [_kikuchi_matrix, _kikuchi_matrix_symb])
+def test_examples(bloq_autotester, bloq_ex):
+ if bloq_autotester.check_name == 'serialize':
+ pytest.skip()
+
+ bloq_autotester(bloq_ex)
+
+
+@pytest.mark.notebook
+def test_notebook():
+ qlt_testing.execute_notebook('kikuchi_block_encoding')
+
+
+def test_controlled_cost():
+ bloq = _kikuchi_matrix()
+ _, sigma = bloq.call_graph(max_depth=2)
+ _, ctrl_sigma = bloq.controlled().call_graph(max_depth=2)
+
+ assert set(sigma.items()) - set(ctrl_sigma.items()) == {(Swap(32), 1), (Swap(1), 1)}
+ assert set(ctrl_sigma.items()) - set(sigma.items()) == {
+ (Swap(32).controlled(), 1),
+ (Swap(1).controlled(), 1),
+ }
+
+
+def test_cost():
+ bloq = _kikuchi_matrix()
+
+ _ = get_cost_value(bloq, QECGatesCost())
+
+
+def test_cost_symb():
+ bloq = _kikuchi_matrix_symb()
+
+ _ = get_cost_value(bloq, QECGatesCost())
+ print(_)
diff --git a/qualtran/bloqs/optimization/k_xor_sat/load_kxor_instance.ipynb b/qualtran/bloqs/optimization/k_xor_sat/load_kxor_instance.ipynb
new file mode 100644
index 000000000..7987d624e
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/load_kxor_instance.ipynb
@@ -0,0 +1,207 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "448cdbc3",
+ "metadata": {
+ "cq.autogen": "title_cell"
+ },
+ "source": [
+ "# kXOR: Instance load Oracles\n",
+ "\n",
+ "We define three oracles that load a kXOR instance, which are used in the algorithm.\n",
+ "\n",
+ "We are given a kXOR instance $\\mathcal{I}$ of $n$ variables,\n",
+ "with $\\bar{m}$ unique scopes $\\{U_j | j \\in [\\bar{m}]\\}$.\n",
+ "We provide oracles to:\n",
+ "1. `LoadConstraintScopes`: Given $j \\in [\\bar{m}]$, compute $U_j$.\n",
+ "2. `LoadUniqueScopeIndex`: Given $U_j$, compute $j \\in [\\bar{m}]$\n",
+ "3. `PRGAUniqueConstraintRHS` Given $j$, apply $Rx(arccos(\\sqrt{B_\\mathcal{I}(S)/M}))$ on a target qubit.\n",
+ "(for an appropriate normalization $M$).\n",
+ "\n",
+ "\n",
+ "The first two oracles are independent of the RHS.\n",
+ "All these oracles can output arbitrary values for invalid inputs.\n",
+ "\n",
+ "References:\n",
+ " [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1)\n",
+ " Notation 2.24 for $B_\\mathcal{I}$.\n",
+ " Theorem 4.17, proof para 2 for $U_j$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "611e4ef6",
+ "metadata": {
+ "cq.autogen": "top_imports"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran import Bloq, CompositeBloq, BloqBuilder, Signature, Register\n",
+ "from qualtran import QBit, QInt, QUInt, QAny\n",
+ "from qualtran.drawing import show_bloq, show_call_graph, show_counts_sigma\n",
+ "from typing import *\n",
+ "import numpy as np\n",
+ "import sympy\n",
+ "import cirq"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b5e118d0",
+ "metadata": {
+ "cq.autogen": "LoadConstraintScopes.bloq_doc.md"
+ },
+ "source": [
+ "## `LoadConstraintScopes`\n",
+ "Given an index $j$, load the scope of the $j$-th unique constraint.\n",
+ "\n",
+ "Given a $k$-XOR-SAT instance `inst` with $n$ variables and $m$ constraints.\n",
+ "Assuming `inst` has $\\bar{m}$ unique constraints, we define $U_j \\in {[n] \\choose k}$\n",
+ "for $j \\in [\\bar{m}]$ as the $j$-th unique constraint scope.\n",
+ "\n",
+ "The scopes are loaded using a QROM.\n",
+ "\n",
+ "If the input contains an invalid index, then any arbitrary value can be output.\n",
+ "\n",
+ "#### Registers\n",
+ " - `j`: a number in [\\bar{m}]\n",
+ " - `U`: $j$-th unique scope\n",
+ " - `ancilla`: entangled intermediate qubits, to be uncomputed by the adjoint. \n",
+ "\n",
+ "#### References\n",
+ " - [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1). Theorem 4.17, proof para 2.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "51cbd971",
+ "metadata": {
+ "cq.autogen": "LoadConstraintScopes.bloq_doc.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.optimization.k_xor_sat import LoadConstraintScopes"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "45f7354e",
+ "metadata": {
+ "cq.autogen": "LoadConstraintScopes.example_instances.md"
+ },
+ "source": [
+ "### Example Instances"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "137d0cb6",
+ "metadata": {
+ "cq.autogen": "LoadConstraintScopes.load_scopes_symb"
+ },
+ "outputs": [],
+ "source": [
+ "import sympy\n",
+ "\n",
+ "from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import KXorInstance\n",
+ "\n",
+ "n, m, k = sympy.symbols(\"n m k\", positive=True, integer=True)\n",
+ "inst = KXorInstance.symbolic(n=n, m=m, k=k)\n",
+ "load_scopes_symb = LoadConstraintScopes(inst)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "d1a93c7c",
+ "metadata": {
+ "cq.autogen": "LoadConstraintScopes.load_scopes"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import Constraint, KXorInstance\n",
+ "\n",
+ "inst = KXorInstance(\n",
+ " n=6,\n",
+ " k=4,\n",
+ " constraints=(\n",
+ " Constraint(S=(0, 1, 2, 3), b=1),\n",
+ " Constraint(S=(0, 1, 4, 5), b=-1),\n",
+ " Constraint(S=(1, 2, 4, 5), b=1),\n",
+ " Constraint(S=(0, 3, 4, 5), b=1),\n",
+ " Constraint(S=(2, 3, 4, 5), b=1),\n",
+ " Constraint(S=(0, 1, 2, 3), b=1),\n",
+ " Constraint(S=(0, 3, 4, 5), b=1),\n",
+ " Constraint(S=(2, 3, 4, 5), b=1),\n",
+ " ),\n",
+ ")\n",
+ "load_scopes = LoadConstraintScopes(inst)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "107c977f",
+ "metadata": {
+ "cq.autogen": "LoadConstraintScopes.graphical_signature.md"
+ },
+ "source": [
+ "#### Graphical Signature"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "3a998692",
+ "metadata": {
+ "cq.autogen": "LoadConstraintScopes.graphical_signature.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.drawing import show_bloqs\n",
+ "show_bloqs([load_scopes_symb, load_scopes],\n",
+ " ['`load_scopes_symb`', '`load_scopes`'])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8b3ac93d",
+ "metadata": {
+ "cq.autogen": "LoadConstraintScopes.call_graph.md"
+ },
+ "source": [
+ "### Call Graph"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "29b2841a",
+ "metadata": {
+ "cq.autogen": "LoadConstraintScopes.call_graph.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.resource_counting.generalizers import ignore_split_join\n",
+ "load_scopes_symb_g, load_scopes_symb_sigma = load_scopes_symb.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
+ "show_call_graph(load_scopes_symb_g)\n",
+ "show_counts_sigma(load_scopes_symb_sigma)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "name": "python"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/qualtran/bloqs/optimization/k_xor_sat/load_kxor_instance.py b/qualtran/bloqs/optimization/k_xor_sat/load_kxor_instance.py
new file mode 100644
index 000000000..3d379f974
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/load_kxor_instance.py
@@ -0,0 +1,354 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+r"""We define three oracles that load a kXOR instance, which are used in the algorithm.
+
+We are given a kXOR instance $\mathcal{I}$ of $n$ variables,
+with $\bar{m}$ unique scopes $\{U_j | j \in [\bar{m}]\}$.
+We provide oracles to:
+1. `LoadConstraintScopes`: Given $j \in [\bar{m}]$, compute $U_j$.
+2. `LoadUniqueScopeIndex`: Given $U_j$, compute $j \in [\bar{m}]$
+3. `PRGAUniqueConstraintRHS` Given $j$, apply $Rx(arccos(\sqrt{B_\mathcal{I}(S)/M}))$ on a target qubit.
+(for an appropriate normalization $M$).
+
+
+The first two oracles are independent of the RHS.
+All these oracles can output arbitrary values for invalid inputs.
+
+References:
+ [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1)
+ Notation 2.24 for $B_\mathcal{I}$.
+ Theorem 4.17, proof para 2 for $U_j$.
+"""
+from functools import cached_property
+from typing import Counter, Sequence, Union
+
+import attrs
+import numpy as np
+from attrs import frozen
+
+from qualtran import (
+ AddControlledT,
+ Bloq,
+ bloq_example,
+ BloqBuilder,
+ BloqDocSpec,
+ BQUInt,
+ CtrlSpec,
+ DecomposeTypeError,
+ QAny,
+ QBit,
+ QFxp,
+ Register,
+ Side,
+ Signature,
+ Soquet,
+ SoquetT,
+)
+from qualtran.bloqs.arithmetic import EqualsAConstant, LessThanConstant
+from qualtran.bloqs.basic_gates import Hadamard, SGate
+from qualtran.bloqs.bookkeeping import Partition
+from qualtran.bloqs.data_loading import QROM
+from qualtran.bloqs.rotations.rz_via_phase_gradient import RzViaPhaseGradient
+from qualtran.resource_counting import BloqCountDictT, SympySymbolAllocator
+from qualtran.symbolics import ceil, HasLength, is_symbolic, is_zero, log2, SymbolicInt
+
+from .kxor_instance import KXorInstance
+
+
+@frozen
+class LoadConstraintScopes(Bloq):
+ r"""Given an index $j$, load the scope of the $j$-th unique constraint.
+
+ Given a $k$-XOR-SAT instance `inst` with $n$ variables and $m$ constraints.
+ Assuming `inst` has $\bar{m}$ unique constraints, we define $U_j \in {[n] \choose k}$
+ for $j \in [\bar{m}]$ as the $j$-th unique constraint scope.
+
+ The scopes are loaded using a QROM.
+
+ If the input contains an invalid index, then any arbitrary value can be output.
+
+ Registers:
+ j: a number in [\bar{m}]
+ U (RIGHT): $j$-th unique scope
+ ancilla (RIGHT): entangled intermediate qubits, to be uncomputed by the adjoint.
+
+ References:
+ [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1)
+ Theorem 4.17, proof para 2.
+ """
+
+ inst: KXorInstance
+
+ @cached_property
+ def signature(self) -> 'Signature':
+ registers: list[Register] = [
+ Register('j', self.m_dtype),
+ Register('U', QAny(self.scope_bitsize), side=Side.RIGHT),
+ ]
+
+ if not is_zero(self.ancilla_bitsize):
+ registers.append(Register('ancilla', QAny(self.ancilla_bitsize), side=Side.RIGHT))
+
+ return Signature(registers)
+
+ @cached_property
+ def scope_bitsize(self) -> SymbolicInt:
+ """total number of bits to store `k` indices in `[n]`."""
+ return self.inst.k * self.inst.index_bitsize
+
+ @cached_property
+ def ancilla_bitsize(self) -> SymbolicInt:
+ """ancillas used by the underlying QRO(A)M"""
+ return 0
+
+ @cached_property
+ def m_dtype(self):
+ r"""number of bits to store $j \in [\bar{m}]$."""
+ m = self.inst.num_unique_constraints
+ bitsize = ceil(log2(m))
+ return BQUInt(bitsize, m)
+
+ @cached_property
+ def _qrom_bloq(self) -> QROM:
+ # TODO use QROAMClean?
+
+ if self.inst.is_symbolic():
+ return QROM.build_from_bitsize(self.inst.num_unique_constraints, self.scope_bitsize)
+
+ assert isinstance(self.inst.batched_scopes, tuple)
+ scopes = np.array([S for S, _ in self.inst.batched_scopes], dtype=int)
+ assert scopes.shape == (self.inst.num_unique_constraints, self.inst.k)
+ return QROM.build_from_data(
+ *scopes.T, target_bitsizes=(self.inst.index_bitsize,) * self.inst.k
+ )
+
+ def build_composite_bloq(self, bb: 'BloqBuilder', j: 'Soquet') -> dict[str, 'SoquetT']:
+ if self.inst.is_symbolic():
+ raise DecomposeTypeError(f"cannot decompose symbolic {self}")
+
+ targets = {
+ f'target{i}_': bb.allocate(self.inst.index_bitsize) for i in range(int(self.inst.k))
+ }
+ targets = bb.add_d(self._qrom_bloq, selection=j, **targets)
+ j = targets.pop('selection')
+
+ U = bb.add(
+ Partition(self.scope_bitsize, self._qrom_bloq.target_registers).adjoint(), **targets
+ )
+ return {'j': j, 'U': U}
+
+ def build_call_graph(self, ssa: 'SympySymbolAllocator') -> BloqCountDictT:
+ return {self._qrom_bloq: 1}
+
+
+@bloq_example
+def _load_scopes() -> LoadConstraintScopes:
+ from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import Constraint, KXorInstance
+
+ inst = KXorInstance(
+ n=6,
+ k=4,
+ constraints=(
+ Constraint(S=(0, 1, 2, 3), b=1),
+ Constraint(S=(0, 1, 4, 5), b=-1),
+ Constraint(S=(1, 2, 4, 5), b=1),
+ Constraint(S=(0, 3, 4, 5), b=1),
+ Constraint(S=(2, 3, 4, 5), b=1),
+ Constraint(S=(0, 1, 2, 3), b=1),
+ Constraint(S=(0, 3, 4, 5), b=1),
+ Constraint(S=(2, 3, 4, 5), b=1),
+ ),
+ )
+ load_scopes = LoadConstraintScopes(inst)
+ return load_scopes
+
+
+@bloq_example
+def _load_scopes_symb() -> LoadConstraintScopes:
+ import sympy
+
+ from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import KXorInstance
+
+ n, m, k = sympy.symbols("n m k", positive=True, integer=True)
+ inst = KXorInstance.symbolic(n=n, m=m, k=k)
+ load_scopes_symb = LoadConstraintScopes(inst)
+ return load_scopes_symb
+
+
+_LOAD_INSTANCE_DOC = BloqDocSpec(
+ bloq_cls=LoadConstraintScopes, examples=[_load_scopes_symb, _load_scopes]
+)
+
+
+@frozen
+class LoadUniqueScopeIndex(Bloq):
+ r"""Given a scope $S$, load $j$ such that $S = U_j$, the $j$-th unique scope.
+
+ If the input contains an invalid scope, then any arbitrary value can be output.
+
+ Registers:
+ S: A scope $S \in {[n] \choose k}$.
+ j (RIGHT): a number in $[\bar{m}]$ s.t. $S = U_j$.
+ ancilla (RIGHT): entangled intermediate qubits, to be uncomputed by the adjoint.
+ """
+
+ inst: KXorInstance
+
+ @cached_property
+ def signature(self) -> 'Signature':
+ return Signature.build_from_dtypes(j=self.m_dtype, U=QAny(self.scope_bitsize))
+
+ @cached_property
+ def scope_bitsize(self) -> SymbolicInt:
+ """total number of bits to store `k` indices in `[n]`."""
+ return self.inst.k * self.inst.index_bitsize
+
+ @cached_property
+ def m_dtype(self):
+ r"""number of bits to store $j \in [\bar{m}]$."""
+ m = self.inst.num_unique_constraints
+ bitsize = ceil(log2(m))
+ return BQUInt(bitsize, m)
+
+ def build_call_graph(self, ssa: 'SympySymbolAllocator') -> BloqCountDictT:
+ counts = Counter[Bloq]()
+
+ c = ssa.new_symbol("c")
+ counts[EqualsAConstant(self.scope_bitsize, c)] += self.inst.num_unique_constraints
+
+ return counts
+
+
+@frozen
+class PRGAUniqueConstraintRHS(Bloq):
+ r"""Map $|j\rangle |0\rangle$ to $|j\rangle (\sqrt{E_j} |0\rangle + \sqrt{1 - |E_j|}|1\rangle)$
+
+ Given an instance $\mathcal{I}$, with unique scopes $U_j$ and corresponding RHS values
+ $E_j = B_\mathcal{I}(U_j)/M$ (where $M$ is the max. abs. entry, usually 2)
+ apply the above rotation on the target qubit.
+
+ This is done by first rotating for $|E_j|$ (i.e. ignoring the sign),
+ by loading the values $\arccos{\sqrt{|E_j|}} / (2 * \pi)$,
+ and applying an `Rx` using an `RzViaPhaseGradient` surrounded by `H`.
+
+ We then apply the sign correction of $i$ for the negative entries by an $S$ gate.
+ We ensure that the input data is sorted, therefore we can simply compare $j$
+ with the largest negative index, and apply a `CS` gate.
+
+ Args:
+ inst: kXOR instance $\mathcal{I}$.
+ angle_bitsize: number of bits to load the amplitude rotation angles to.
+
+ Registers:
+ j: Selection index, loads the value of $E_j = B_\mathcal{I}(U_j)/M$
+ q: rotation target.
+ """
+
+ inst: KXorInstance
+ angle_bitsize: SymbolicInt
+ is_controlled: bool = False
+
+ @cached_property
+ def signature(self) -> 'Signature':
+ return Signature.build_from_dtypes(ctrl=QAny(self.n_ctrl), j=self.m_dtype, q=QBit())
+
+ @property
+ def n_ctrl(self) -> int:
+ return 1 if self.is_controlled else 0
+
+ @cached_property
+ def m_dtype(self):
+ r"""number of bits to store $j \in [\bar{m}]$."""
+ m = self.inst.num_unique_constraints
+ bitsize = ceil(log2(m))
+ return BQUInt(bitsize, m)
+
+ @cached_property
+ def _angle_dtype(self):
+ return QFxp(self.angle_bitsize, self.angle_bitsize)
+
+ @cached_property
+ def _qrom_angle_data(
+ self,
+ ) -> tuple[Union[HasLength, Sequence[int]], Union[HasLength, Sequence[int]]]:
+ M = self.inst.max_rhs
+ scopes = self.inst.batched_scopes
+ if is_symbolic(M) or is_symbolic(scopes):
+ m = self.inst.num_unique_constraints
+ return HasLength(m), HasLength(m)
+
+ b = [b for _, b in scopes]
+ assert np.all(b == np.sort(b)), "data must be sorted!"
+
+ amplitude_angles = np.arccos(np.sqrt(np.abs(b) / M))
+ amplitude_angles_int = np.round(amplitude_angles * 2**self.angle_bitsize)
+
+ signs = tuple(np.sign(b))
+ return amplitude_angles_int, signs
+
+ @cached_property
+ def _amplitude_qrom(self) -> QROM:
+ data, _ = self._qrom_angle_data
+ if is_symbolic(data):
+ return QROM.build_from_bitsize(
+ data_len_or_shape=self.inst.num_unique_constraints,
+ target_bitsizes=self.angle_bitsize,
+ num_controls=self.n_ctrl,
+ )
+
+ return QROM.build_from_data(
+ data, target_bitsizes=(self.angle_bitsize,), num_controls=self.n_ctrl
+ )
+
+ @cached_property
+ def _num_negative(self) -> SymbolicInt:
+ """returns $k$ s.t. the first $k$ elements are negative."""
+ _, signs = self._qrom_angle_data
+ if is_symbolic(signs):
+ return self.inst.num_unique_constraints // 2
+
+ assert np.all(signs == np.sort(signs)), "data must be sorted!"
+ return int(np.searchsorted(signs, 0))
+
+ def build_call_graph(self, ssa: 'SympySymbolAllocator') -> BloqCountDictT:
+ counts = Counter[Bloq]()
+
+ # load the amplitudes
+ counts[self._amplitude_qrom] += 1
+
+ # apply a Rx rotation using Rx = H Rz H
+ counts[Hadamard()] += 2
+ counts[RzViaPhaseGradient(self._angle_dtype, self._angle_dtype)] += 1
+
+ # apply the sign correction
+ # TODO use the half-bloq once implemented to wire this correctly
+ sign_compare = LessThanConstant(self.m_dtype.num_qubits, self._num_negative)
+ counts[sign_compare] += 1
+ counts[SGate().controlled()] += 1
+
+ # unload amplitudes
+ counts[self._amplitude_qrom.adjoint()] += 1
+
+ return counts
+
+ def get_ctrl_system(self, ctrl_spec: 'CtrlSpec') -> tuple['Bloq', 'AddControlledT']:
+ from qualtran.bloqs.mcmt.specialized_ctrl import get_ctrl_system_1bit_cv_from_bloqs
+
+ return get_ctrl_system_1bit_cv_from_bloqs(
+ self,
+ ctrl_spec,
+ current_ctrl_bit=1 if self.is_controlled else None,
+ bloq_with_ctrl=self if self.is_controlled else attrs.evolve(self, is_controlled=True),
+ ctrl_reg_name='ctrl',
+ )
diff --git a/qualtran/bloqs/optimization/k_xor_sat/load_kxor_instance_test.py b/qualtran/bloqs/optimization/k_xor_sat/load_kxor_instance_test.py
new file mode 100644
index 000000000..97f833b45
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/load_kxor_instance_test.py
@@ -0,0 +1,49 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+from unittest.mock import ANY
+
+import pytest
+
+from qualtran import Bloq
+from qualtran.resource_counting import GateCounts, get_cost_value, QECGatesCost
+
+from .load_kxor_instance import _load_scopes, _load_scopes_symb
+
+
+@pytest.mark.parametrize("bloq", [_load_scopes, _load_scopes_symb])
+def test_examples(bloq_autotester, bloq: Bloq):
+ if bloq_autotester.check_name == 'serialize':
+ pytest.skip()
+
+ bloq_autotester(bloq)
+
+
+def test_load_instance():
+ bloq = _load_scopes()
+
+ gc = get_cost_value(bloq, QECGatesCost())
+ assert gc == GateCounts(and_bloq=3, clifford=ANY, measurement=ANY)
+
+ # classical action
+ for j, (S, _) in enumerate(tuple(bloq.inst.batched_scopes)): # type: ignore
+ assert bloq.call_classically(j=j) == (j, bloq.inst.scope_as_int(S))
+
+
+def test_load_instance_cost_symb():
+ bloq = _load_scopes_symb()
+
+ m, k = bloq.inst.m, bloq.inst.k
+ logn = bloq.inst.index_bitsize
+ gc = get_cost_value(bloq, QECGatesCost())
+ assert gc == GateCounts(and_bloq=m - 2, clifford=k * m * logn + m - 2, measurement=m - 2)
diff --git a/qualtran/bloqs/optimization/k_xor_sat/planted_noisy_kxor.ipynb b/qualtran/bloqs/optimization/k_xor_sat/planted_noisy_kxor.ipynb
new file mode 100644
index 000000000..b946aade8
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/planted_noisy_kxor.ipynb
@@ -0,0 +1,235 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "ee412c69",
+ "metadata": {
+ "cq.autogen": "title_cell"
+ },
+ "source": [
+ "# Algorithm: Planted Noise kXOR"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "df5a7866",
+ "metadata": {
+ "cq.autogen": "top_imports"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran import Bloq, CompositeBloq, BloqBuilder, Signature, Register\n",
+ "from qualtran import QBit, QInt, QUInt, QAny\n",
+ "from qualtran.drawing import show_bloq, show_call_graph, show_counts_sigma\n",
+ "from typing import *\n",
+ "import numpy as np\n",
+ "import sympy\n",
+ "import cirq"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "36559e8d",
+ "metadata": {
+ "cq.autogen": "PlantedNoisyKXOR.bloq_doc.md"
+ },
+ "source": [
+ "## `PlantedNoisyKXOR`\n",
+ "Algorithm for Planted Noisy kXOR.\n",
+ "\n",
+ "Problem (Problem 2.6 of Ref [1]):\n",
+ "\n",
+ "Given a noisy-kXOR instance $\\hat{\\mathcal{I}}$ which is drawn either:\n",
+ "\n",
+ "1. with planted advantage $\\rho$, from $\\tilde\\mathcal{P}^{z}_{n, k}(m, \\rho)$.\n",
+ "2. at random, from $\\tilde\\mathcal{R}_{n, k}(m)$.\n",
+ "\n",
+ "output a single bit such that it is whp `1` in case 1, and `0` in case 2.\n",
+ "\n",
+ "Algorithm (Section 4.4, Theorem 4.18):\n",
+ "We first split the instance into $\\hat{\\mathcal{I}} = \\mathcal{I} \\cup \\mathcal{I}_\\text{guide}$,\n",
+ "by placing each constraint independently in $\\mathcal{I}$ with prob. $1 - \\zeta$,\n",
+ "otherwise in $\\mathcal{I}_\\text{guide}$.\n",
+ "$\\zeta$ is picked to be $1 / \\ln n$.\n",
+ "\n",
+ "#### Parameters\n",
+ " - `inst_guide`: The subset of contraints $\\mathcal{I}_\\text{guide}$ for the guided state.\n",
+ " - `inst_solve`: The subset of constraints $\\mathcal{I}$ for eigenvalue estimation.\n",
+ " - `ell`: Kikuchi parameter $\\ell$.\n",
+ " - `rho`: the planted advantage $\\rho$ in the planted case. \n",
+ "\n",
+ "#### References\n",
+ " - [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1). \n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "f930da5f",
+ "metadata": {
+ "cq.autogen": "PlantedNoisyKXOR.bloq_doc.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.optimization.k_xor_sat import PlantedNoisyKXOR"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "18f43abd",
+ "metadata": {
+ "cq.autogen": "PlantedNoisyKXOR.example_instances.md"
+ },
+ "source": [
+ "### Example Instances"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "1a28aa9c",
+ "metadata": {
+ "cq.autogen": "PlantedNoisyKXOR.solve_planted_symbolic"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.optimization.k_xor_sat import KXorInstance\n",
+ "from qualtran.symbolics import HasLength\n",
+ "\n",
+ "n, m = sympy.symbols(\"n m\", positive=True, integer=True)\n",
+ "k = sympy.symbols(\"k\", positive=True, integer=True, even=True)\n",
+ "c = sympy.symbols(\"c\", positive=True, integer=True)\n",
+ "ell = c * k\n",
+ "rho = sympy.Symbol(r\"\\rho\", positive=True, real=True)\n",
+ "\n",
+ "inst = KXorInstance.symbolic(n, m, k)\n",
+ "zeta = 1 / ln(n)\n",
+ "solve_planted_symbolic = PlantedNoisyKXOR(\n",
+ " inst_guide=inst.subset(HasLength((1 - zeta) * m)),\n",
+ " inst_solve=inst.subset(HasLength(zeta * m)),\n",
+ " ell=ell,\n",
+ " rho=rho,\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "2df9b4ea",
+ "metadata": {
+ "cq.autogen": "PlantedNoisyKXOR.solve_planted"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.optimization.k_xor_sat import KXorInstance\n",
+ "\n",
+ "rng = np.random.default_rng(42)\n",
+ "n, m, k = 50, 1000, 4\n",
+ "ell = k\n",
+ "rho = 0.8\n",
+ "\n",
+ "inst = KXorInstance.random_instance(n, m, k, planted_advantage=rho, rng=rng)\n",
+ "solve_planted = PlantedNoisyKXOR.from_inst(inst, ell=ell, rho=rho, zeta=0.1, rng=rng)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "505c1e9c",
+ "metadata": {
+ "cq.autogen": "PlantedNoisyKXOR.graphical_signature.md"
+ },
+ "source": [
+ "#### Graphical Signature"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "2ead66fe",
+ "metadata": {
+ "cq.autogen": "PlantedNoisyKXOR.graphical_signature.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.drawing import show_bloqs\n",
+ "show_bloqs([solve_planted_symbolic, solve_planted],\n",
+ " ['`solve_planted_symbolic`', '`solve_planted`'])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "bd068fb3",
+ "metadata": {
+ "cq.autogen": "PlantedNoisyKXOR.call_graph.md"
+ },
+ "source": [
+ "### Call Graph"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "946fca15",
+ "metadata": {
+ "cq.autogen": "PlantedNoisyKXOR.call_graph.py"
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.resource_counting.generalizers import ignore_split_join\n",
+ "solve_planted_symbolic_g, solve_planted_symbolic_sigma = solve_planted_symbolic.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
+ "show_call_graph(solve_planted_symbolic_g)\n",
+ "show_counts_sigma(solve_planted_symbolic_sigma)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "id": "2c8e9045-060a-4386-99be-5af7ee653fd6",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "#### Counts totals:\n",
+ " - `Adjoint(subbloq=GuidedHamiltonianPhaseEstimation)`: $\\displaystyle \\left\\lceil{\\frac{202.020202020202 c^{0.5} k^{0.5} \\left(c k\\right)^{\\frac{c k}{2}}}{Part_{k}(\\ell)^{0.5} \\rho^{0.5} \\left(\\frac{\\left(\\frac{m \\left(1 - \\frac{1}{\\operatorname{log}_{2}{\\left(n \\right)}}\\right) + \\frac{m}{\\operatorname{log}_{2}{\\left(n \\right)}}}{{\\binom{n}{k}}}\\right)^{c} \\left(\\frac{\\rho^{2} m}{\\left(m \\left(1 - \\frac{1}{\\operatorname{log}_{2}{\\left(n \\right)}}\\right) + \\frac{m}{\\operatorname{log}_{2}{\\left(n \\right)}}\\right) \\operatorname{log}_{2}{\\left(n \\right)}}\\right)^{c}}{\\log{\\left(n \\right)}^{2}}\\right)^{0.5}}}\\right\\rceil$\n",
+ " - `GuidedHamiltonianPhaseEstimation`: $\\displaystyle \\left\\lceil{\\frac{202.020202020202 c^{0.5} k^{0.5} \\left(c k\\right)^{\\frac{c k}{2}}}{Part_{k}(\\ell)^{0.5} \\rho^{0.5} \\left(\\frac{\\left(\\frac{m \\left(1 - \\frac{1}{\\operatorname{log}_{2}{\\left(n \\right)}}\\right) + \\frac{m}{\\operatorname{log}_{2}{\\left(n \\right)}}}{{\\binom{n}{k}}}\\right)^{c} \\left(\\frac{\\rho^{2} m}{\\left(m \\left(1 - \\frac{1}{\\operatorname{log}_{2}{\\left(n \\right)}}\\right) + \\frac{m}{\\operatorname{log}_{2}{\\left(n \\right)}}\\right) \\operatorname{log}_{2}{\\left(n \\right)}}\\right)^{c}}{\\log{\\left(n \\right)}^{2}}\\right)^{0.5}}}\\right\\rceil + 1$\n",
+ " - `MultiControlZ`: $\\displaystyle \\left\\lceil{\\frac{202.020202020202 c^{0.5} k^{0.5} \\left(c k\\right)^{\\frac{c k}{2}}}{Part_{k}(\\ell)^{0.5} \\rho^{0.5} \\left(\\frac{\\left(\\frac{m \\left(1 - \\frac{1}{\\operatorname{log}_{2}{\\left(n \\right)}}\\right) + \\frac{m}{\\operatorname{log}_{2}{\\left(n \\right)}}}{{\\binom{n}{k}}}\\right)^{c} \\left(\\frac{\\rho^{2} m}{\\left(m \\left(1 - \\frac{1}{\\operatorname{log}_{2}{\\left(n \\right)}}\\right) + \\frac{m}{\\operatorname{log}_{2}{\\left(n \\right)}}\\right) \\operatorname{log}_{2}{\\left(n \\right)}}\\right)^{c}}{\\log{\\left(n \\right)}^{2}}\\right)^{0.5}}}\\right\\rceil$\n",
+ " - `ZGate`: $\\displaystyle \\left\\lceil{\\frac{202.020202020202 c^{0.5} k^{0.5} \\left(c k\\right)^{\\frac{c k}{2}}}{Part_{k}(\\ell)^{0.5} \\rho^{0.5} \\left(\\frac{\\left(\\frac{m \\left(1 - \\frac{1}{\\operatorname{log}_{2}{\\left(n \\right)}}\\right) + \\frac{m}{\\operatorname{log}_{2}{\\left(n \\right)}}}{{\\binom{n}{k}}}\\right)^{c} \\left(\\frac{\\rho^{2} m}{\\left(m \\left(1 - \\frac{1}{\\operatorname{log}_{2}{\\left(n \\right)}}\\right) + \\frac{m}{\\operatorname{log}_{2}{\\left(n \\right)}}\\right) \\operatorname{log}_{2}{\\left(n \\right)}}\\right)^{c}}{\\log{\\left(n \\right)}^{2}}\\right)^{0.5}}}\\right\\rceil$"
+ ],
+ "text/plain": [
+ "<IPython.core.display.Markdown object>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "_, sigma = solve_planted_symbolic.call_graph(max_depth=2, generalizer=ignore_split_join)\n",
+ "show_counts_sigma(sigma) # inverse of Eq. 150"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.11.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/qualtran/bloqs/optimization/k_xor_sat/planted_noisy_kxor.py b/qualtran/bloqs/optimization/k_xor_sat/planted_noisy_kxor.py
new file mode 100644
index 000000000..865e34946
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/planted_noisy_kxor.py
@@ -0,0 +1,424 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+from functools import cached_property
+from typing import Optional
+
+import numpy as np
+import scipy
+import sympy
+from attrs import field, frozen
+
+from qualtran import Bloq, bloq_example, BloqBuilder, BloqDocSpec, Signature, SoquetT
+from qualtran.bloqs.state_preparation.black_box_prepare import BlackBoxPrepare
+from qualtran.bloqs.state_preparation.prepare_base import PrepareOracle
+from qualtran.resource_counting import BloqCountDictT, SympySymbolAllocator
+from qualtran.symbolics import (
+ ceil,
+ HasLength,
+ is_symbolic,
+ ln,
+ log2,
+ prod,
+ slen,
+ ssqrt,
+ SymbolicFloat,
+ SymbolicInt,
+)
+
+from .guided_hamiltonian import GuidedHamiltonian
+from .kikuchi_block_encoding import KikuchiHamiltonian
+from .kikuchi_guiding_state import GuidingState, SimpleGuidingState
+from .kxor_instance import KXorInstance
+
+
+def comb(n: SymbolicInt, k: SymbolicInt) -> SymbolicInt:
+ """compute n choose k"""
+ if is_symbolic(n, k):
+ return sympy.binomial(n, k)
+ return scipy.special.comb(n, k)
+
+
+@frozen(kw_only=True)
+class KikuchiAverageDegreeTheorem:
+ """Compute the average degree of the Kikuchi matrix.
+
+ The Alice theorem (Thm 2.21) guarantees this with high probability
+ for random/planted instances.
+ """
+
+ n: SymbolicInt
+ k: SymbolicInt
+ ell: SymbolicInt
+
+ @cached_property
+ def delta(self) -> SymbolicFloat:
+ """Eq 19"""
+ n, k, l = self.n, self.k, self.ell
+ term_1 = comb(k, k // 2)
+ term_2 = comb(n - k, l - k // 2) / comb(n, l)
+ return term_1 * term_2
+
+
+@frozen(kw_only=True)
+class AliceTheorem:
+ r"""Alice theorem, E.g. Theorem 2.21.
+
+ Consider a $k$XOR instance over $n$ variables and $m$ clauses, with Kikuchi parameter $\ell$.
+
+ Assume:
+ - $\ell \ge k/2$
+ - $n \gg k \ell$
+
+ For any parameters $\kappa \le 1$ and $0 < \epsilon \le \kappa/(2+\kappa)$,
+ assume: $m$ satisfies
+ $m/n \ge C_\kappa (n/\ell)^{(k-2)/2}$
+ where
+ $C_\kappa = 2(1+\epsilon)(1+\kappa) \kappa^{-2} {k \choose k/2}^{-1} \ln n$
+
+ Then for a randomly drawn instance $\mathcal{I}$ (i.e. advantage 0),
+ except with probability $3 n^{-\epsilon \ell}$, we are guaranteed:
+
+ $\lambda_\max{\mathcal{K}_\ell(\mathcal{I})} \le \kappa d$
+ where
+ $d = \delta_{\ell,n,k} m$.
+
+ Args:
+ n: number of variables $n$
+ k: number of variables per equation $k$
+ ell: Kikuchi parameter
+ kappa: parameter $\kappa$
+ eps: parameter $\epsilon$
+
+ References:
+ [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1)
+ """
+
+ n: int
+ k: int
+ ell: int
+ kappa: float
+ eps: float = field()
+
+ @eps.default
+ def _default_max_eps(self):
+ return self.kappa / (2 + self.kappa)
+
+ def __attrs_post_init__(self):
+ assert self.k % 2 == 0, "k must be even"
+ assert self.ell % self.k == 0, "l must be a multiple of k"
+ # assert self.n >= self.k * self.ell, "n must be atleast lk"
+ assert 0 <= self.kappa <= 1
+ assert 0 < self.eps <= self.kappa / (2 + self.kappa)
+
+ @cached_property
+ def C_kappa(self):
+ """Eq 20 (right)"""
+ term_1 = 2 * (1 + self.eps) * (1 + self.kappa) / self.kappa**2
+ term_2 = comb(self.k, self.k // 2)
+ term_3 = np.log(self.n)
+
+ value = (term_1 / term_2) * term_3
+ return value
+
+ @cached_property
+ def fail_prob(self):
+ return 3 / self.n ** (self.eps * self.ell)
+
+ @cached_property
+ def min_m(self):
+ """Eq 20 (left)"""
+ m = self.C_kappa * (self.n / self.ell) ** (self.k // 2) * self.ell
+ return ceil(m)
+
+
+@frozen(kw_only=True)
+class GuidingStateOverlapTheorem:
+ r"""Lower-bound the overlap of the prepared guiding state with the eigenspace.
+
+ This is an implementation of Theorem 2.40.
+
+ Args:
+ n: number of variables
+ k: number of variables per constraint
+ m_hat: total number of constraints
+ ell: kikuchi parameter $\ell$
+ zeta: the probability of picking a constraint for $\mathcal{I}_\text{guide}$.
+ nu: parameter in $(0, .99]$.
+ eps: parameter.
+ rho: planted advantage.
+
+ References:
+ [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1)
+ Section 2.7, Theorem 2.40.
+ """
+
+ n: SymbolicInt
+ k: SymbolicInt
+ m_hat: SymbolicInt
+ ell: SymbolicInt
+ zeta: SymbolicFloat
+ nu: SymbolicFloat
+ eps: SymbolicFloat
+ rho: SymbolicFloat
+
+ @cached_property
+ def part_k_l(self) -> SymbolicInt:
+ ell, k = self.ell, self.k
+ if is_symbolic(ell) or is_symbolic(k):
+ return sympy.Symbol(r"Part_{k}(\ell)", positive=True, integer=True)
+ return prod([comb(ell - i * k, k) for i in range(ell // k)])
+
+ @cached_property
+ def xi(self):
+ r"""Eq 60 $\xi$"""
+ term_1 = self.part_k_l
+ term_2 = (self.rho * self.eps * self.nu) / (200 * self.ell * ln(self.n))
+ term_3 = (self.rho**2 * self.zeta) ** (self.ell // self.k)
+ return term_1 * term_2 * term_3
+
+ @cached_property
+ def overlap_probability(self) -> SymbolicFloat:
+ term_2_base = self.m_hat / comb(self.n, self.k)
+ term_2 = term_2_base ** (self.ell / self.k)
+ return self.xi * term_2
+
+
+@frozen
+class PlantedNoisyKXOR(Bloq):
+ r"""Algorithm for Planted Noisy kXOR.
+
+ Problem (Problem 2.6 of Ref [1]):
+
+ Given a noisy-kXOR instance $\hat{\mathcal{I}}$ which is drawn either:
+
+ 1. with planted advantage $\rho$, from $\tilde\mathcal{P}^{z}_{n, k}(m, \rho)$.
+ 2. at random, from $\tilde\mathcal{R}_{n, k}(m)$.
+
+ output a single bit such that it is whp `1` in case 1, and `0` in case 2.
+
+ Algorithm (Section 4.4, Theorem 4.18):
+ We first split the instance into $\hat{\mathcal{I}} = \mathcal{I} \cup \mathcal{I}_\text{guide}$,
+ by placing each constraint independently in $\mathcal{I}$ with prob. $1 - \zeta$,
+ otherwise in $\mathcal{I}_\text{guide}$.
+ $\zeta$ is picked to be $1 / \ln n$.
+
+ Args:
+ inst_guide: The subset of contraints $\mathcal{I}_\text{guide}$ for the guided state.
+ inst_solve: The subset of constraints $\mathcal{I}$ for eigenvalue estimation.
+ ell: Kikuchi parameter $\ell$.
+ rho: the planted advantage $\rho$ in the planted case.
+
+ References:
+ [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1)
+ """
+
+ inst_guide: KXorInstance
+ inst_solve: KXorInstance
+ ell: SymbolicInt
+ rho: SymbolicFloat
+ _guiding_state_overlap: Optional[SymbolicFloat] = field(kw_only=True, default=None)
+
+ def __attrs_post_init__(self):
+ k = self.inst_guide.k
+ if not is_symbolic(k):
+ assert k % 2 == 0, f"{k=} must be even"
+
+ ell = self.ell
+ if not is_symbolic(k, ell):
+ assert ell % k == 0 and ell >= k, f"{ell=} must be a multiple of {k=}"
+
+ @cached_property
+ def signature(self) -> 'Signature':
+ return self.guided_hamiltonian_bloq.signature
+
+ @classmethod
+ def from_inst(
+ cls,
+ inst: KXorInstance,
+ ell: SymbolicInt,
+ rho: SymbolicFloat,
+ *,
+ rng: np.random.Generator,
+ zeta: Optional[SymbolicFloat] = None,
+ guiding_state_overlap: Optional[SymbolicFloat] = None,
+ ):
+ if zeta is None:
+ zeta = 1 / log2(inst.n)
+
+ (use_for_guide,) = np.nonzero(np.atleast_1d(rng.random(inst.m) < zeta))
+ inst_guide = inst.subset(tuple(use_for_guide))
+
+ if is_symbolic(inst, use_for_guide):
+ inst_solve = inst.subset(HasLength(inst.m - slen(use_for_guide)))
+ else:
+ mask = np.ones(inst.m)
+ mask[np.array(use_for_guide)] = 0
+ (rest,) = np.nonzero(mask)
+ inst_solve = inst.subset(tuple(rest))
+
+ return cls(
+ inst_guide=inst_guide,
+ inst_solve=inst_solve,
+ ell=ell,
+ rho=rho,
+ guiding_state_overlap=guiding_state_overlap,
+ )
+
+ @cached_property
+ def guiding_state_and_coefficient(self) -> tuple[PrepareOracle, SymbolicFloat]:
+ r"""Return a bloq that prepares the guiding state, and its coefficient.
+
+ If the bloq prepares $\beta |\Psi\rangle|0\rangle + |\perp\rangle|1\rangle$,
+ then this will return $|\beta|$.
+
+ The returned $\beta$ is an theoretical lower bound on the true value,
+ and is correct for $1 - o(1)$ fraction of random instances.
+ """
+ if self.ell == self.inst_guide.k:
+ return SimpleGuidingState(inst=self.inst_guide), 1
+ bloq = GuidingState(inst=self.inst_guide, ell=self.ell)
+ return bloq, bloq.amplitude_good_part
+
+ @cached_property
+ def guiding_state_overlap_guarantee(self) -> GuidingStateOverlapTheorem:
+ """Invoke Theorem 2.40 to obtain a lower bound on the guiding state overlap.
+
+ The below parameters are picked from Theorem 4.18, proof para 2.
+ """
+ n, k = self.inst_guide.n, self.inst_guide.k
+ m_guide = self.inst_guide.m
+ m_solve = self.inst_solve.m
+ m_hat = m_guide + m_solve
+ zeta = m_solve / m_hat
+ return GuidingStateOverlapTheorem(
+ n=n, k=k, ell=self.ell, m_hat=m_hat, zeta=zeta, nu=1 / ln(n), eps=0.005, rho=self.rho
+ )
+
+ @cached_property
+ def guiding_state_overlap(self) -> SymbolicFloat:
+ if self._guiding_state_overlap is not None:
+ return self.guiding_state_overlap
+ _, guiding_state_good_coeff = self.guiding_state_and_coefficient
+ return guiding_state_good_coeff
+
+ @cached_property
+ def overlap(self) -> SymbolicFloat:
+ # guiding state
+ guiding_state_good_coeff = self.guiding_state_overlap
+
+ # overlap of |\Gamma(A)> with the threshold eigenspace
+ overlap_good_eigen = self.guiding_state_overlap_guarantee.overlap_probability**0.5
+
+ # total overlap is the sqrt probability of the ancilla being 0,
+ # and the state being in the >= lambda eigenspace.
+ overlap = guiding_state_good_coeff * overlap_good_eigen
+
+ return overlap
+
+ @cached_property
+ def degree_guarantee(self) -> KikuchiAverageDegreeTheorem:
+ return KikuchiAverageDegreeTheorem(n=self.inst_solve.n, k=self.inst_solve.k, ell=self.ell)
+
+ @cached_property
+ def sparsity(self) -> SymbolicInt:
+ """sparsity of the kikuchi matrix, $d$"""
+ # d = \delta m
+ d = self.degree_guarantee.delta * self.inst_solve.m
+ if is_symbolic(d):
+ return d # type: ignore
+ return ceil(d)
+
+ @cached_property
+ def hamiltonian(self) -> KikuchiHamiltonian:
+ return KikuchiHamiltonian(
+ inst=self.inst_solve, ell=self.ell, entry_bitsize=10, s=self.sparsity
+ )
+
+ @cached_property
+ def guided_hamiltonian_bloq(self) -> GuidedHamiltonian:
+ # Thm 4.18 proof para 2.
+ # lambda = 0.995 rho d
+ eigenvalue_threshold = 0.995 * self.rho * self.sparsity
+
+ kappa = 0.99 * self.rho
+ eps = 0.005
+
+ # Thm 4.18 proof para 3
+ # kappa' <= (1 - alpha) lambda
+ # ==> alpha <= 1 - kappa'/lambda
+ # we pick kappa' s.t. it satisfies the alice theorem for inst_solve.m
+ # simple approximation: kappa' = kappa / sqrt(1-zeta)
+ zeta = self.inst_guide.m / (self.inst_guide.m + self.inst_solve.m)
+ kappa_prime = kappa / ssqrt(1 - zeta)
+ alpha = 1 - kappa_prime / eigenvalue_threshold
+ if not is_symbolic(alpha):
+ assert alpha > 0, f"got negative {alpha=}"
+
+ guiding_state, _ = self.guiding_state_and_coefficient
+
+ return GuidedHamiltonian(
+ self.hamiltonian,
+ BlackBoxPrepare(guiding_state),
+ lambd=eigenvalue_threshold,
+ alpha=alpha,
+ gamma=self.overlap,
+ )
+
+ def build_composite_bloq(self, bb: 'BloqBuilder', **soqs: 'SoquetT') -> dict[str, 'SoquetT']:
+ soqs = bb.add_d(self.guided_hamiltonian_bloq, **soqs)
+ return soqs
+
+ def build_call_graph(self, ssa: 'SympySymbolAllocator') -> BloqCountDictT:
+ return {self.guided_hamiltonian_bloq: 1}
+
+
+@bloq_example
+def _solve_planted() -> PlantedNoisyKXOR:
+ from qualtran.bloqs.optimization.k_xor_sat import KXorInstance
+
+ rng = np.random.default_rng(42)
+ n, m, k = 50, 1000, 4
+ ell = k
+ rho = 0.8
+
+ inst = KXorInstance.random_instance(n, m, k, planted_advantage=rho, rng=rng)
+ solve_planted = PlantedNoisyKXOR.from_inst(inst, ell=ell, rho=rho, zeta=0.1, rng=rng)
+ return solve_planted
+
+
+@bloq_example
+def _solve_planted_symbolic() -> PlantedNoisyKXOR:
+ from qualtran.bloqs.optimization.k_xor_sat import KXorInstance
+ from qualtran.symbolics import HasLength
+
+ n, m = sympy.symbols("n m", positive=True, integer=True)
+ k = sympy.symbols("k", positive=True, integer=True, even=True)
+ c = sympy.symbols("c", positive=True, integer=True)
+ ell = c * k
+ rho = sympy.Symbol(r"\rho", positive=True, real=True)
+
+ inst = KXorInstance.symbolic(n, m, k)
+ zeta = 1 / ln(n)
+ solve_planted_symbolic = PlantedNoisyKXOR(
+ inst_guide=inst.subset(HasLength((1 - zeta) * m)),
+ inst_solve=inst.subset(HasLength(zeta * m)),
+ ell=ell,
+ rho=rho,
+ )
+ return solve_planted_symbolic
+
+
+_PLANTED_NOISY_KXOR_DOC = BloqDocSpec(
+ bloq_cls=PlantedNoisyKXOR, examples=[_solve_planted_symbolic, _solve_planted]
+)
diff --git a/qualtran/bloqs/optimization/k_xor_sat/planted_noisy_kxor_test.py b/qualtran/bloqs/optimization/k_xor_sat/planted_noisy_kxor_test.py
new file mode 100644
index 000000000..37a415332
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/planted_noisy_kxor_test.py
@@ -0,0 +1,116 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+import numpy as np
+import pytest
+import sympy
+
+from qualtran.drawing import show_call_graph
+from qualtran.resource_counting import get_cost_value, QECGatesCost
+from qualtran.resource_counting.generalizers import ignore_alloc_free, ignore_split_join
+from qualtran.symbolics import ln, log2
+
+from .kxor_instance import KXorInstance
+from .planted_noisy_kxor import (
+ _solve_planted,
+ _solve_planted_symbolic,
+ AliceTheorem,
+ PlantedNoisyKXOR,
+)
+
+
+@pytest.fixture
+def rng():
+ return np.random.default_rng(42)
+
+
+@pytest.mark.xfail
+def test_alice_thm_symb():
+ n, m = sympy.symbols("n m", positive=True, integer=True)
+ k = sympy.symbols("k", positive=True, integer=True, even=True)
+ rho = sympy.symbols(r"\rho", positive=True, real=True)
+ c = sympy.symbols(r"c", positive=True, integer=True)
+ thm = AliceTheorem(n=n, k=k, ell=c * k, kappa=0.99 * rho, eps=0.005)
+ _ = thm.C_kappa()
+ _ = thm.min_m()
+ _ = thm.fail_prob()
+
+
+@pytest.mark.parametrize("bloq_ex", [_solve_planted, _solve_planted_symbolic])
+def test_examples(bloq_autotester, bloq_ex):
+ if bloq_autotester.check_name == 'serialize':
+ pytest.skip()
+
+ bloq_autotester(bloq_ex)
+
+
+def test_call_graph():
+ _solve_planted().call_graph()
+
+
+def test_call_graph_symb():
+ algo = _solve_planted_symbolic()
+ g, sigma = algo.call_graph(generalizer=[ignore_split_join, ignore_alloc_free])
+ show_call_graph(g)
+
+
+def example_random_instance(*, k=4, n=100, m=1000, c=2, rho=0.8, seed=120) -> PlantedNoisyKXOR:
+ # generate instance
+ rng = np.random.default_rng(seed)
+ ell = c * k
+ inst = KXorInstance.random_instance(n=n, m=m, k=k, planted_advantage=rho, rng=rng)
+ algo_bloq = PlantedNoisyKXOR.from_inst(inst=inst, ell=ell, rho=rho, zeta=1 / ln(n), rng=rng)
+
+ return algo_bloq
+
+
+def test_gate_cost():
+ bloq = example_random_instance()
+ gc = get_cost_value(bloq, QECGatesCost())
+ t_cost = gc.total_t_count(ts_per_cswap=4)
+
+ n = bloq.inst_guide.n
+ m = bloq.inst_guide.m + bloq.inst_solve.m
+ ell = bloq.ell
+ c = ell // bloq.inst_guide.k
+
+ big_O_expected = n ** (ell / 4) * (m**0.5) * ell**ell * log2(n) ** (c // 2)
+ print()
+ print(t_cost)
+ print(t_cost / big_O_expected)
+ print(big_O_expected)
+ print(t_cost / big_O_expected * bloq.guiding_state_overlap)
+ print(1 / bloq.guiding_state_overlap)
+ print(1 / bloq.guiding_state_overlap_guarantee.overlap_probability**0.5)
+
+
+@pytest.mark.parametrize("n", [40, 50, 60, 70, 80, 90, 100])
+@pytest.mark.parametrize("k", [4, 8])
+@pytest.mark.parametrize("c", [2, 3, 4])
+def test_more_costs(n, k, c):
+ if c * k == 32 and n <= 40:
+ pytest.skip("too small n")
+
+ bloq = example_random_instance(k=k, c=c, n=n, m=n, seed=142)
+ cost = get_cost_value(bloq, QECGatesCost())
+ print(cost)
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize("n", [10**4, 10**5])
+def test_large(n):
+ k = 4
+ c = 32 // 4
+ bloq = example_random_instance(k=k, c=c, n=n, m=n * 10, seed=142)
+ cost = get_cost_value(bloq, QECGatesCost())
+ print(cost)
diff --git a/qualtran/bloqs/optimization/k_xor_sat/shims.py b/qualtran/bloqs/optimization/k_xor_sat/shims.py
new file mode 100644
index 000000000..720998180
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/shims.py
@@ -0,0 +1,77 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+from typing import Optional
+
+import attrs
+
+from qualtran import Bloq, CtrlSpec, Signature
+from qualtran.resource_counting import CostKey, GateCounts, QECGatesCost
+from qualtran.symbolics import SymbolicInt
+
+
+@attrs.frozen
+class ArbitraryGate(Bloq):
+ """Placeholder gate for costing
+
+ Footnote 18, page 29:
+ By “gate complexity”, we mean the total number of (arbitrary) 1- and 2-qubit gates
+ used by the quantum algorithm. These gates can be further represented using a
+ finite universal gate set with a logarithmic overhead.
+
+ References:
+ [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1)
+ Section 4.4.2 for algorithm. Section 2.4 for definitions and notation.
+ """
+
+ n_ctrls: SymbolicInt = 0
+
+ @property
+ def signature(self) -> 'Signature':
+ return Signature.build(q=1 + self.n_ctrls)
+
+ def my_static_costs(self, cost_key: 'CostKey'):
+ if isinstance(cost_key, QECGatesCost):
+ # placeholder cost: reduce controls to single bit, and use C-SU2 (say).
+ return GateCounts(rotation=1, and_bloq=self.n_ctrls)
+
+ return NotImplemented
+
+ def adjoint(self) -> 'Bloq':
+ return self
+
+ def get_ctrl_system(self, ctrl_spec: CtrlSpec):
+ ctrl_bloq = attrs.evolve(self, n_ctrls=self.n_ctrls + ctrl_spec.num_qubits)
+
+ return ctrl_bloq, NotImplemented
+
+
+def generalize_1_2_qubit_gates(b: Bloq) -> Optional[Bloq]:
+ from qualtran.bloqs.basic_gates import GlobalPhase, Identity
+ from qualtran.bloqs.bookkeeping import ArbitraryClifford
+ from qualtran.resource_counting.classify_bloqs import (
+ bloq_is_clifford,
+ bloq_is_rotation,
+ bloq_is_t_like,
+ )
+
+ if bloq_is_t_like(b) or bloq_is_clifford(b) or bloq_is_rotation(b):
+ return ArbitraryGate()
+
+ if isinstance(b, ArbitraryClifford):
+ return ArbitraryGate()
+
+ if isinstance(b, (GlobalPhase, Identity)):
+ return None
+
+ return b
diff --git a/qualtran/bloqs/optimization/k_xor_sat/tutorial_planted_noisy_kxor.py.ipynb b/qualtran/bloqs/optimization/k_xor_sat/tutorial_planted_noisy_kxor.py.ipynb
new file mode 100644
index 000000000..e72a1ed87
--- /dev/null
+++ b/qualtran/bloqs/optimization/k_xor_sat/tutorial_planted_noisy_kxor.py.ipynb
@@ -0,0 +1,2526 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "f9ab6a67-1a3c-459f-9716-cda924fa4efe",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "eceae6a5-5497-4ea9-8c24-0abd0f45554c",
+ "metadata": {},
+ "source": [
+ "### Implementing [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d5eb2c1f-a57d-4b18-8b26-454da506578b",
+ "metadata": {},
+ "source": [
+ "### Problem Definition"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f6e0f089-9c57-4d87-8478-5b6660cb6395",
+ "metadata": {},
+ "source": [
+ "**Definition 2.2 (simplified):**\n",
+ "A kXOR instance $\\mathcal{I}$ on $n$ variables in ${0, 1}$ is a collection of $m$ constraints, each of the form\n",
+ "$$ x_{c_1} \\oplus x_{c_2} \\oplus ... x_{c_k} = b $$ "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ebd9642b-99a2-4ee4-b905-826174d5a8c7",
+ "metadata": {},
+ "source": [
+ "**Notation 2.3**\n",
+ "Random Instance: Pick each clause independently:\n",
+ "- Pick $C$, a $k$ subset of $[n] = \\{1, ... n\\}$ uniformly at random.\n",
+ "- Pick $b \\in {0, 1}$ uniformly at random."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "1756cf95-b8ad-42ca-bb35-59528bf96538",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.max_k_xor_sat import KXorInstance, Constraint\n",
+ "\n",
+ "n, k = 10, 4\n",
+ "cs = (\n",
+ " Constraint((0, 1, 2, 3), -1), # read: x_0 ^ x_1 ^ x_2 ^ x_3 = 0\n",
+ " Constraint((0, 2, 4, 5), 1),\n",
+ " Constraint((0, 3, 4, 5), 1),\n",
+ " Constraint((0, 3, 4, 5), 1),\n",
+ " Constraint((1, 2, 3, 4), -1),\n",
+ " Constraint((1, 3, 4, 5), -1),\n",
+ " Constraint((1, 3, 4, 5), -1),\n",
+ " Constraint((2, 3, 4, 5), 1),\n",
+ ")\n",
+ "simple_inst = KXorInstance(n, k, cs)\n",
+ "simple_inst"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5fc71a1f-e1d4-44fb-b657-8d43af87626f",
+ "metadata": {},
+ "source": [
+ "**Notation 2.4 (simplified)** Planted Instance:\n",
+ "Given $\\rho \\in [0, 1]$ (the _planted advantage_),\n",
+ "\n",
+ "first pick a secret assignment $z \\in \\{0, 1\\}^n$.\n",
+ "Now pick each clause independently by: \n",
+ "- Pick $C$, a $k$ subset of $[n]$ uniformly at random.\n",
+ "- Pick noise $\\eta \\in {0, 1}$, s.t. $\\eta = 0$ with probability $(1 + \\rho)/2$\n",
+ "- Set $b = C(z) \\oplus \\eta$\n",
+ "\n",
+ "Note: when $\\rho = 0$, the noise is random, and when $\\rho = 1$, there is no noise."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "2d334a8e-3792-4ece-9f9c-d77da3111aa2",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "random_inst = KXorInstance.random_instance(\n",
+ " n=10, \n",
+ " m=20, \n",
+ " k=4,\n",
+ " planted_advantage=0.8,\n",
+ " rng=np.random.default_rng(42),\n",
+ ")\n",
+ "random_inst"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cd35802e-1778-44de-81bd-9356da3999a7",
+ "metadata": {},
+ "source": [
+ "## Problem\n",
+ "\n",
+ "**Problem 2.6 (Planted Noisy kXOR)**\n",
+ "Given $\\rho \\in (0, 1)$, and an instance $\\mathcal{I}$ that is promised to be either drawn from the random distribution or planted distribution (with $\\rho$), distinguish which case it is."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4e401d1e-157c-4f49-adfe-9ceeb315ba6d",
+ "metadata": {},
+ "source": [
+ "## Kikuchi Method\n",
+ "This is a technique to reduce $k$XOR problems to $2$XOR problems, on an exponentially larger set of variables (say, $O(n^k)$).\n",
+ "The 2XOR is known to be efficiently solvable by some spectral analysis.\n",
+ "\n",
+ "For this, we pick our new variables as subsets of $[n]$ of size $k$, call them $X_S$ for each subset $S$.\n",
+ "There are ${n \\choose k}$ variables now, and for $k \\ll n$, this is about $O(n^k)$.\n",
+ "\n",
+ "The equations are of the form $X_S \\oplus X_T = b(S, T)$ for every $S, T$ with $|S \\Delta T| = k$.\n",
+ "Here $b(S, T)$ is the xor of all variables in S and T (common ones cancel out, leaving only the $k$ as above)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "da3f5e5c-67dd-4717-962b-23052fdd30ad",
+ "metadata": {},
+ "source": [
+ "## Quantum Algorithm\n",
+ "\n",
+ "**Theorem 4.18 (simplified)**\n",
+ "Let $k$ (even) and $\\rho \\in (0, 1)$ be known constants.\n",
+ "\n",
+ "We are given an instance $\\mathcal{I}$ which is either random or planted (with advantage $\\rho$),\n",
+ "where the number of constraints $m$ is picked above a given threshold (see Alice Theorem).\n",
+ "\n",
+ "For a parameter $\\ell$, if we have a classical _Kikuchi style_ algorithm with complexity $\\tilde{O}(n^\\ell)$,\n",
+ "then there is a quantum algorithm with $\\tilde{O}(n^{\\ell/4} m \\ell^{O{\\ell}} \\log^{\\ell/2k}n)$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "id": "9b5a6bbb-e895-47d9-8ea6-5ab1f07329e3",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-08-27T13:03:40.693090Z",
+ "start_time": "2024-08-27T13:03:38.179464Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from qualtran.bloqs.max_k_xor_sat.planted_noisy_kxor import PlantedNoisyKXOR\n",
+ "from qualtran.drawing import show_bloq, show_call_graph, show_counts_sigma"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "id": "b5e3a55c-00a9-40a4-b309-79fa008b0760",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-08-27T13:03:40.693090Z",
+ "start_time": "2024-08-27T13:03:38.179464Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def make_algo_example():\n",
+ " k = 4\n",
+ " n, m = 100, 1000\n",
+ " rho = 0.8\n",
+ " \n",
+ " c = 2 # Kikuchi param: ell = c * k\n",
+ " \n",
+ " # generate instance\n",
+ " rng = np.random.default_rng(142)\n",
+ " ell = c * k\n",
+ " inst = KXorInstance.random_instance(n=n, m=m, k=k, planted_advantage=rho, rng=rng)\n",
+ " algo_bloq = PlantedNoisyKXOR.from_inst(inst=inst, ell=ell, rho=rho, zeta=1 / np.log(n), rng=rng)\n",
+ "\n",
+ " expected_complexity = n ** (ell/4) * m * ell**ell * np.log(n)**(c//2)\n",
+ "\n",
+ " return algo_bloq, expected_complexity"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "id": "46dc55f4-3873-40a2-9509-b723493eeb85",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "bloq, cost_O_tilde = make_algo_example()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "id": "04de6797-5986-461e-b040-2ec7fab2bcc2",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
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+ "id": "6cdc8096-84da-4358-b068-1e4438be51e4",
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+ "<polygon fill=\"black\" stroke=\"black\" points=\"4184.85,-111.63 4174.72,-114.75 4184.58,-118.63 4184.85,-111.63\"/>\n",
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+ "<title>b29</title>\n",
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+ "<text text-anchor=\"start\" x=\"5487.75\" y=\"-106.95\" font-family=\"Times,serif\" font-size=\"14.00\">PhaseGradientUnitary</text>\n",
+ "<text text-anchor=\"start\" x=\"5406\" y=\"-96.75\" font-family=\"monospace\" font-size=\"10.00\">bitsize=4, exponent=0.5, is_controlled=True, eps=1e-10</text>\n",
+ "</g>\n",
+ "<!-- b12->b29 -->\n",
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+ "<title>b12->b29</title>\n",
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+ "<title>b30</title>\n",
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+ "<text text-anchor=\"start\" x=\"6227.75\" y=\"-106.95\" font-family=\"Times,serif\" font-size=\"14.00\">PhaseGradientUnitary</text>\n",
+ "<text text-anchor=\"start\" x=\"6146\" y=\"-96.75\" font-family=\"monospace\" font-size=\"10.00\">bitsize=2, exponent=0.5, is_controlled=True, eps=1e-10</text>\n",
+ "</g>\n",
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+ "<g id=\"edge25\" class=\"edge\">\n",
+ "<title>b12->b30</title>\n",
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+ "<polygon fill=\"black\" stroke=\"black\" points=\"6311.5,-136.97 6308,-126.97 6304.5,-136.97 6311.5,-136.97\"/>\n",
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+ "<title>b31</title>\n",
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+ "<text text-anchor=\"start\" x=\"6842.75\" y=\"-106.95\" font-family=\"Times,serif\" font-size=\"14.00\">PhaseGradientUnitary</text>\n",
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+ "</g>\n",
+ "<!-- b12->b31 -->\n",
+ "<g id=\"edge27\" class=\"edge\">\n",
+ "<title>b12->b31</title>\n",
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+ "<title>b38</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"9197.5,-125.25 9106.5,-125.25 9106.5,-89.25 9197.5,-89.25 9197.5,-125.25\"/>\n",
+ "<text text-anchor=\"start\" x=\"9114.5\" y=\"-102.58\" font-family=\"Times,serif\" font-size=\"14.00\">Hadamard</text>\n",
+ "</g>\n",
+ "<!-- b12->b38 -->\n",
+ "<g id=\"edge20\" class=\"edge\">\n",
+ "<title>b12->b38</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M6400.42,-195.19C6741.36,-193.58 7960.71,-183.82 8964,-125.25 9008.03,-122.68 9057.72,-118.11 9094.95,-114.36\"/>\n",
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+ "<title>b45</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"9479.62,-125.25 9374.38,-125.25 9374.38,-89.25 9479.62,-89.25 9479.62,-125.25\"/>\n",
+ "<text text-anchor=\"start\" x=\"9382.38\" y=\"-102.58\" font-family=\"Times,serif\" font-size=\"14.00\">TwoBitSwap</text>\n",
+ "</g>\n",
+ "<!-- b12->b45 -->\n",
+ "<g id=\"edge26\" class=\"edge\">\n",
+ "<title>b12->b45</title>\n",
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+ "<title>b32</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"11772,-125.25 11636,-125.25 11636,-89.25 11772,-89.25 11772,-125.25\"/>\n",
+ "<text text-anchor=\"start\" x=\"11684.12\" y=\"-106.95\" font-family=\"Times,serif\" font-size=\"14.00\">B[H]†</text>\n",
+ "<text text-anchor=\"start\" x=\"11644\" y=\"-96.75\" font-family=\"monospace\" font-size=\"10.00\">subbloq=KikuchiH ...</text>\n",
+ "</g>\n",
+ "<!-- b13->b32 -->\n",
+ "<g id=\"edge49\" class=\"edge\">\n",
+ "<title>b13->b32</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M11318.85,-178.05C11347.26,-164.52 11384.77,-147.4 11401,-143.25 11493.47,-119.6 11520.44,-138.22 11615,-125.25 11618.04,-124.83 11621.13,-124.38 11624.24,-123.9\"/>\n",
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+ "<g id=\"node48\" class=\"node\">\n",
+ "<title>b47</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"11606,-125.25 11164,-125.25 11164,-89.25 11606,-89.25 11606,-125.25\"/>\n",
+ "<text text-anchor=\"start\" x=\"11299.88\" y=\"-106.95\" font-family=\"Times,serif\" font-size=\"14.00\">ReflectionUsingPrepare</text>\n",
+ "<text text-anchor=\"start\" x=\"11172\" y=\"-96.75\" font-family=\"monospace\" font-size=\"10.00\">prepare_gate=BlackBox ..., control_val=None, global_phase=-1, eps=1e-11</text>\n",
+ "</g>\n",
+ "<!-- b13->b47 -->\n",
+ "<g id=\"edge50\" class=\"edge\">\n",
+ "<title>b13->b47</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M11303.15,-178.26C11318.38,-165.24 11339.48,-147.18 11356.45,-132.67\"/>\n",
+ "<polygon fill=\"black\" stroke=\"black\" points=\"11358.42,-135.6 11363.74,-126.44 11353.87,-130.28 11358.42,-135.6\"/>\n",
+ "<text text-anchor=\"middle\" x=\"11347.5\" y=\"-147.2\" font-family=\"Times,serif\" font-size=\"14.00\">1</text>\n",
+ "</g>\n",
+ "<!-- b33 -->\n",
+ "<g id=\"node34\" class=\"node\">\n",
+ "<title>b33</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"8955.25,-125.25 8718.75,-125.25 8718.75,-89.25 8955.25,-89.25 8955.25,-125.25\"/>\n",
+ "<text text-anchor=\"start\" x=\"8726.75\" y=\"-106.95\" font-family=\"Times,serif\" font-size=\"14.00\">StatePreparationViaRotations†</text>\n",
+ "<text text-anchor=\"start\" x=\"8777\" y=\"-96.75\" font-family=\"monospace\" font-size=\"10.00\">subbloq=StatePre ...</text>\n",
+ "</g>\n",
+ "<!-- b14->b33 -->\n",
+ "<g id=\"edge61\" class=\"edge\">\n",
+ "<title>b14->b33</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M9660.18,-178.12C9630.23,-165.94 9587.84,-150.58 9549,-143.25 9450.44,-124.65 9198.16,-130.51 9098,-125.25 9055.32,-123.01 9008.74,-120.12 8966.9,-117.36\"/>\n",
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+ "<text text-anchor=\"middle\" x=\"9616.5\" y=\"-147.2\" font-family=\"Times,serif\" font-size=\"14.00\">1</text>\n",
+ "</g>\n",
+ "<!-- b34 -->\n",
+ "<g id=\"node35\" class=\"node\">\n",
+ "<title>b34</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"613,-125.25 477,-125.25 477,-89.25 613,-89.25 613,-125.25\"/>\n",
+ "<text text-anchor=\"start\" x=\"494.38\" y=\"-106.95\" font-family=\"Times,serif\" font-size=\"14.00\">GuidingState†</text>\n",
+ "<text text-anchor=\"start\" x=\"485\" y=\"-96.75\" font-family=\"monospace\" font-size=\"10.00\">subbloq=GuidingS ...</text>\n",
+ "</g>\n",
+ "<!-- b15->b34 -->\n",
+ "<g id=\"edge75\" class=\"edge\">\n",
+ "<title>b15->b34</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1325.6,-188.47C1169.95,-172.47 789.99,-133.43 624.36,-116.41\"/>\n",
+ "<polygon fill=\"black\" stroke=\"black\" points=\"625.1,-112.96 614.8,-115.42 624.39,-119.93 625.1,-112.96\"/>\n",
+ "<text text-anchor=\"middle\" x=\"1050.5\" y=\"-147.2\" font-family=\"Times,serif\" font-size=\"14.00\">1</text>\n",
+ "</g>\n",
+ "<!-- b51 -->\n",
+ "<g id=\"node52\" class=\"node\">\n",
+ "<title>b51</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"1673,-125.25 1423,-125.25 1423,-89.25 1673,-89.25 1673,-125.25\"/>\n",
+ "<text text-anchor=\"start\" x=\"1516.88\" y=\"-106.95\" font-family=\"Times,serif\" font-size=\"14.00\">Partition</text>\n",
+ "<text text-anchor=\"start\" x=\"1431\" y=\"-96.75\" font-family=\"monospace\" font-size=\"10.00\">n=56, regs=(Registe ..., partition=True</text>\n",
+ "</g>\n",
+ "<!-- b15->b51 -->\n",
+ "<g id=\"edge74\" class=\"edge\">\n",
+ "<title>b15->b51</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1424.79,-178.05C1448.51,-164.62 1481.49,-145.93 1507.37,-131.27\"/>\n",
+ "<polygon fill=\"black\" stroke=\"black\" points=\"1508.97,-134.39 1515.94,-126.41 1505.52,-128.3 1508.97,-134.39\"/>\n",
+ "<text text-anchor=\"middle\" x=\"1489.5\" y=\"-147.2\" font-family=\"Times,serif\" font-size=\"14.00\">1</text>\n",
+ "</g>\n",
+ "<!-- b52 -->\n",
+ "<g id=\"node53\" class=\"node\">\n",
+ "<title>b52</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"1137,-125.25 881,-125.25 881,-89.25 1137,-89.25 1137,-125.25\"/>\n",
+ "<text text-anchor=\"start\" x=\"977.88\" y=\"-106.95\" font-family=\"Times,serif\" font-size=\"14.00\">Partition</text>\n",
+ "<text text-anchor=\"start\" x=\"889\" y=\"-96.75\" font-family=\"monospace\" font-size=\"10.00\">n=27, regs=(Registe ..., partition=False</text>\n",
+ "</g>\n",
+ "<!-- b15->b52 -->\n",
+ "<g id=\"edge76\" class=\"edge\">\n",
+ "<title>b15->b52</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1325.61,-180C1261.82,-165.55 1166.34,-143.91 1096.91,-128.17\"/>\n",
+ "<polygon fill=\"black\" stroke=\"black\" points=\"1098.01,-124.83 1087.48,-126.04 1096.46,-131.66 1098.01,-124.83\"/>\n",
+ "<text text-anchor=\"middle\" x=\"1240.5\" y=\"-147.2\" font-family=\"Times,serif\" font-size=\"14.00\">1</text>\n",
+ "</g>\n",
+ "<!-- b53 -->\n",
+ "<g id=\"node54\" class=\"node\">\n",
+ "<title>b53</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"1405,-125.25 1155,-125.25 1155,-89.25 1405,-89.25 1405,-125.25\"/>\n",
+ "<text text-anchor=\"start\" x=\"1248.88\" y=\"-106.95\" font-family=\"Times,serif\" font-size=\"14.00\">Partition</text>\n",
+ "<text text-anchor=\"start\" x=\"1163\" y=\"-96.75\" font-family=\"monospace\" font-size=\"10.00\">n=27, regs=(Registe ..., partition=True</text>\n",
+ "</g>\n",
+ "<!-- b15->b53 -->\n",
+ "<g id=\"edge77\" class=\"edge\">\n",
+ "<title>b15->b53</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1371.2,-178.05C1354.2,-165.04 1330.74,-147.08 1311.87,-132.64\"/>\n",
+ "<polygon fill=\"black\" stroke=\"black\" points=\"1314.03,-129.88 1303.96,-126.59 1309.77,-135.44 1314.03,-129.88\"/>\n",
+ "<text text-anchor=\"middle\" x=\"1352.5\" y=\"-147.2\" font-family=\"Times,serif\" font-size=\"14.00\">1</text>\n",
+ "</g>\n",
+ "<!-- b54 -->\n",
+ "<g id=\"node55\" class=\"node\">\n",
+ "<title>b54</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"1947,-125.25 1691,-125.25 1691,-89.25 1947,-89.25 1947,-125.25\"/>\n",
+ "<text text-anchor=\"start\" x=\"1787.88\" y=\"-106.95\" font-family=\"Times,serif\" font-size=\"14.00\">Partition</text>\n",
+ "<text text-anchor=\"start\" x=\"1699\" y=\"-96.75\" font-family=\"monospace\" font-size=\"10.00\">n=56, regs=(Registe ..., partition=False</text>\n",
+ "</g>\n",
+ "<!-- b15->b54 -->\n",
+ "<g id=\"edge78\" class=\"edge\">\n",
+ "<title>b15->b54</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M1453.71,-178.1C1493.03,-167.07 1545.79,-153.08 1593,-143.25 1621,-137.42 1651.15,-132.1 1680,-127.46\"/>\n",
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+ "<text text-anchor=\"middle\" x=\"1597.5\" y=\"-147.2\" font-family=\"Times,serif\" font-size=\"14.00\">1</text>\n",
+ "</g>\n",
+ "<!-- b35 -->\n",
+ "<g id=\"node36\" class=\"node\">\n",
+ "<title>b35</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"9356,-125.25 9244,-125.25 9244,-89.25 9356,-89.25 9356,-125.25\"/>\n",
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+ "<text text-anchor=\"start\" x=\"9252\" y=\"-96.75\" font-family=\"monospace\" font-size=\"10.00\">cvs=(1, 1, 1 ...</text>\n",
+ "</g>\n",
+ "<!-- b17->b35 -->\n",
+ "<g id=\"edge89\" class=\"edge\">\n",
+ "<title>b17->b35</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M9300,-178.26C9300,-166.43 9300,-150.45 9300,-136.75\"/>\n",
+ "<polygon fill=\"black\" stroke=\"black\" points=\"9303.5,-136.97 9300,-126.97 9296.5,-136.97 9303.5,-136.97\"/>\n",
+ "<text text-anchor=\"middle\" x=\"9304.5\" y=\"-147.2\" font-family=\"Times,serif\" font-size=\"14.00\">1</text>\n",
+ "</g>\n",
+ "<!-- b36 -->\n",
+ "<g id=\"node37\" class=\"node\">\n",
+ "<title>b36</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"9634,-125.25 9498,-125.25 9498,-89.25 9634,-89.25 9634,-125.25\"/>\n",
+ "<text text-anchor=\"start\" x=\"9529.62\" y=\"-106.95\" font-family=\"Times,serif\" font-size=\"14.00\">MultiAnd†</text>\n",
+ "<text text-anchor=\"start\" x=\"9506\" y=\"-96.75\" font-family=\"monospace\" font-size=\"10.00\">subbloq=MultiAnd ...</text>\n",
+ "</g>\n",
+ "<!-- b18->b36 -->\n",
+ "<g id=\"edge91\" class=\"edge\">\n",
+ "<title>b18->b36</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M9472.49,-178.17C9480.88,-167.3 9492.63,-153.47 9505,-143.25 9510.07,-139.07 9515.7,-135.09 9521.43,-131.43\"/>\n",
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+ "<!-- b37 -->\n",
+ "<g id=\"node38\" class=\"node\">\n",
+ "<title>b37</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"14783,-125.25 14263,-125.25 14263,-89.25 14783,-89.25 14783,-125.25\"/>\n",
+ "<text text-anchor=\"start\" x=\"14416.12\" y=\"-106.95\" font-family=\"Times,serif\" font-size=\"14.00\">StatePreparationViaRotations</text>\n",
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+ "</g>\n",
+ "<!-- b19->b37 -->\n",
+ "<g id=\"edge100\" class=\"edge\">\n",
+ "<title>b19->b37</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M12841.22,-190.82C13104.02,-177.92 13846.67,-141.46 14251.56,-121.58\"/>\n",
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+ "<g id=\"edge112\" class=\"edge\">\n",
+ "<title>b20->b38</title>\n",
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+ "<title>b39</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"18383.62,-125.25 18200.38,-125.25 18200.38,-89.25 18383.62,-89.25 18383.62,-125.25\"/>\n",
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+ "<!-- b20->b39 -->\n",
+ "<g id=\"edge113\" class=\"edge\">\n",
+ "<title>b20->b39</title>\n",
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+ "<text text-anchor=\"middle\" x=\"18865.5\" y=\"-147.2\" font-family=\"Times,serif\" font-size=\"14.00\">1</text>\n",
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+ "<title>b40</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"19349.62,-125.25 19166.38,-125.25 19166.38,-89.25 19349.62,-89.25 19349.62,-125.25\"/>\n",
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+ "<text text-anchor=\"start\" x=\"19198\" y=\"-96.75\" font-family=\"monospace\" font-size=\"10.00\">subbloq=PhaseGra ...</text>\n",
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+ "<g id=\"edge114\" class=\"edge\">\n",
+ "<title>b20->b40</title>\n",
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+ "<polygon fill=\"none\" stroke=\"black\" points=\"13218,-36 13064,-36 13064,0 13218,0 13218,-36\"/>\n",
+ "<text text-anchor=\"start\" x=\"13089.25\" y=\"-17.7\" font-family=\"Times,serif\" font-size=\"14.00\">HasDuplicates</text>\n",
+ "<text text-anchor=\"start\" x=\"13072\" y=\"-7.5\" font-family=\"monospace\" font-size=\"10.00\">l=8, dtype=QUInt(bi ...</text>\n",
+ "</g>\n",
+ "<!-- b55->b132 -->\n",
+ "<g id=\"edge155\" class=\"edge\">\n",
+ "<title>b55->b132</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M12627.28,-96.6C12725.25,-84.5 12896.17,-62.34 13052.46,-36.38\"/>\n",
+ "<polygon fill=\"black\" stroke=\"black\" points=\"13052.9,-39.85 13062.19,-34.75 13051.75,-32.95 13052.9,-39.85\"/>\n",
+ "<text text-anchor=\"middle\" x=\"12933.5\" y=\"-57.95\" font-family=\"Times,serif\" font-size=\"14.00\">1</text>\n",
+ "</g>\n",
+ "<!-- b133 -->\n",
+ "<g id=\"node134\" class=\"node\">\n",
+ "<title>b133</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"13486,-36 13236,-36 13236,0 13486,0 13486,-36\"/>\n",
+ "<text text-anchor=\"start\" x=\"13289\" y=\"-17.7\" font-family=\"Times,serif\" font-size=\"14.00\">SimpleGuidingState</text>\n",
+ "<text text-anchor=\"start\" x=\"13244\" y=\"-7.5\" font-family=\"monospace\" font-size=\"10.00\">inst=KXorInst ..., phasegrad_bitsize=30</text>\n",
+ "</g>\n",
+ "<!-- b55->b133 -->\n",
+ "<g id=\"edge156\" class=\"edge\">\n",
+ "<title>b55->b133</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M12627.31,-106.78C12788.55,-107.12 13146.34,-104 13264,-71.25 13286.13,-65.09 13308.85,-53.21 13326.73,-42.33\"/>\n",
+ "<polygon fill=\"black\" stroke=\"black\" points=\"13328.5,-45.35 13335.11,-37.07 13324.78,-39.42 13328.5,-45.35\"/>\n",
+ "<text text-anchor=\"middle\" x=\"13309.5\" y=\"-57.95\" font-family=\"Times,serif\" font-size=\"14.00\">2</text>\n",
+ "</g>\n",
+ "<!-- b134 -->\n",
+ "<g id=\"node135\" class=\"node\">\n",
+ "<title>b134</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"12452.25,-36 12263.75,-36 12263.75,0 12452.25,0 12452.25,-36\"/>\n",
+ "<text text-anchor=\"start\" x=\"12271.75\" y=\"-17.7\" font-family=\"Times,serif\" font-size=\"14.00\">ProbabilisticUncompute</text>\n",
+ "<text text-anchor=\"start\" x=\"12328\" y=\"-7.5\" font-family=\"monospace\" font-size=\"10.00\">bitsize=24</text>\n",
+ "</g>\n",
+ "<!-- b55->b134 -->\n",
+ "<g id=\"edge157\" class=\"edge\">\n",
+ "<title>b55->b134</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M12466.61,-96.11C12431.6,-90.32 12395.49,-82.04 12382,-71.25 12374.3,-65.09 12368.96,-55.9 12365.32,-46.94\"/>\n",
+ "<polygon fill=\"black\" stroke=\"black\" points=\"12368.73,-46.08 12362.16,-37.77 12362.11,-48.36 12368.73,-46.08\"/>\n",
+ "<text text-anchor=\"middle\" x=\"12386.5\" y=\"-57.95\" font-family=\"Times,serif\" font-size=\"14.00\">1</text>\n",
+ "</g>\n",
+ "<!-- b135 -->\n",
+ "<g id=\"node136\" class=\"node\">\n",
+ "<title>b135</title>\n",
+ "<polygon fill=\"none\" stroke=\"black\" points=\"12624,-36 12470,-36 12470,0 12624,0 12624,-36\"/>\n",
+ "<text text-anchor=\"start\" x=\"12505.38\" y=\"-17.7\" font-family=\"Times,serif\" font-size=\"14.00\">SortInPlace</text>\n",
+ "<text text-anchor=\"start\" x=\"12478\" y=\"-7.5\" font-family=\"monospace\" font-size=\"10.00\">l=8, dtype=QUInt(bi ...</text>\n",
+ "</g>\n",
+ "<!-- b55->b135 -->\n",
+ "<g id=\"edge158\" class=\"edge\">\n",
+ "<title>b55->b135</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M12547,-89.01C12547,-77.18 12547,-61.2 12547,-47.5\"/>\n",
+ "<polygon fill=\"black\" stroke=\"black\" points=\"12550.5,-47.72 12547,-37.72 12543.5,-47.72 12550.5,-47.72\"/>\n",
+ "<text text-anchor=\"middle\" x=\"12551.5\" y=\"-57.95\" font-family=\"Times,serif\" font-size=\"14.00\">1</text>\n",
+ "</g>\n",
+ "</g>\n",
+ "</svg>"
+ ],
+ "text/plain": [
+ "<IPython.core.display.SVG object>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "g, sigma = bloq.call_graph(max_depth=6)\n",
+ "show_call_graph(g)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "id": "234316cd-b790-42ee-baef-d9f08bf2e19d",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'toffoli': 12261972437984,\n",
+ " 'cswap': 5171509416110263,\n",
+ " 'and_bloq': 255058640186620068,\n",
+ " 'clifford': 373887003261338334,\n",
+ " 'rotation': 11450518379588*\\tilde{O}(350784) + 17649125770113,\n",
+ " 'measurement': 255058640186620068}"
+ ]
+ },
+ "execution_count": 24,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from qualtran.resource_counting import get_cost_value, QECGatesCost\n",
+ "\n",
+ "gc = get_cost_value(bloq, QECGatesCost())\n",
+ "gc.asdict()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "id": "a3af760a-c97f-4731-b1d0-5749271f0cdb",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'toffoli': 0.0158706515045947,\n",
+ " 'cswap': 6.69347644605456,\n",
+ " 'and_bloq': 330.121994003046,\n",
+ " 'clifford': 483.921356116957,\n",
+ " 'rotation': 0.0148203878020848*\\tilde{O}(350784) + 0.0228432355295913,\n",
+ " 'measurement': 330.121994003046}"
+ ]
+ },
+ "execution_count": 25,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "(gc * (1/cost_O_tilde)).asdict()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "id": "493750c7-2cd2-40ef-a8b1-f5b52c2a5792",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "'7.726193e+14'"
+ ]
+ },
+ "execution_count": 29,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "f\"{cost_O_tilde:e}\""
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.11.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/qualtran/bloqs/phase_estimation/lp_resource_state.py b/qualtran/bloqs/phase_estimation/lp_resource_state.py
index 53cadba44..f58776ac0 100644
--- a/qualtran/bloqs/phase_estimation/lp_resource_state.py
+++ b/qualtran/bloqs/phase_estimation/lp_resource_state.py
@@ -140,8 +140,9 @@ def from_standard_deviation_eps(cls, eps: SymbolicFloat) -> 'LPResourceState':
def m_bits(self) -> SymbolicInt:
return self.bitsize
- def build_composite_bloq(self, bb: 'BloqBuilder', **soqs: 'SoquetT') -> Dict[str, 'SoquetT']:
- qpe_reg = bb.allocate(dtype=self.m_register.dtype)
+ def build_composite_bloq(
+ self, bb: 'BloqBuilder', qpe_reg: 'Soquet', **soqs: 'SoquetT'
+ ) -> Dict[str, 'SoquetT']:
anc, flag = bb.allocate(dtype=QBit()), bb.allocate(dtype=QBit())
flag_angle = np.arccos(1 / (1 + 2**self.bitsize))
diff --git a/qualtran/bloqs/phase_estimation/qpe_window_state.py b/qualtran/bloqs/phase_estimation/qpe_window_state.py
index 5d6f0c373..eea507d2e 100644
--- a/qualtran/bloqs/phase_estimation/qpe_window_state.py
+++ b/qualtran/bloqs/phase_estimation/qpe_window_state.py
@@ -17,7 +17,7 @@
import attrs
-from qualtran import Bloq, bloq_example, BloqDocSpec, QFxp, Register, Side, Signature
+from qualtran import Bloq, bloq_example, BloqDocSpec, QFxp, Register, Signature
from qualtran.bloqs.basic_gates import Hadamard, OnEach
from qualtran.symbolics import ceil, log2, pi, SymbolicFloat, SymbolicInt
@@ -31,7 +31,7 @@ class QPEWindowStateBase(Bloq, metaclass=abc.ABCMeta):
@cached_property
def m_register(self) -> 'Register':
- return Register('qpe_reg', QFxp(self.m_bits, self.m_bits), side=Side.RIGHT)
+ return Register('qpe_reg', QFxp(self.m_bits, self.m_bits))
@property
@abc.abstractmethod
@@ -95,8 +95,7 @@ def from_standard_deviation_eps(cls, eps: SymbolicFloat):
"""
return cls(ceil(2 * log2(pi(eps) / eps)))
- def build_composite_bloq(self, bb: 'BloqBuilder') -> Dict[str, 'SoquetT']:
- qpe_reg = bb.allocate(dtype=self.m_register.dtype)
+ def build_composite_bloq(self, bb: 'BloqBuilder', qpe_reg) -> Dict[str, 'SoquetT']:
qpe_reg = bb.add(OnEach(self.m_bits, Hadamard()), q=qpe_reg)
return {'qpe_reg': qpe_reg}
diff --git a/qualtran/bloqs/state_preparation/black_box_prepare.py b/qualtran/bloqs/state_preparation/black_box_prepare.py
index 42aacba78..892db1735 100644
--- a/qualtran/bloqs/state_preparation/black_box_prepare.py
+++ b/qualtran/bloqs/state_preparation/black_box_prepare.py
@@ -29,8 +29,7 @@
)
from qualtran.bloqs.bookkeeping.auto_partition import AutoPartition
from qualtran.bloqs.state_preparation.prepare_base import PrepareOracle
-from qualtran.symbolics import ssum, SymbolicFloat, SymbolicInt
-from qualtran.symbolics.types import is_symbolic
+from qualtran.symbolics import is_zero, ssum, SymbolicFloat, SymbolicInt
@frozen
@@ -75,19 +74,19 @@ def signature(self) -> Signature:
return Signature.build(selection=self.selection_bitsize, junk=self.junk_bitsize)
def build_composite_bloq(self, bb: BloqBuilder, **soqs: SoquetT) -> Dict[str, SoquetT]:
- if self.selection_bitsize == 0:
+ if is_zero(self.selection_bitsize):
return soqs
partitions = [
(self.selection_registers[0], [r.name for r in self.prepare.selection_registers])
]
- if is_symbolic(self.junk_bitsize) or self.junk_bitsize > 0:
+ if not is_zero(self.junk_bitsize):
partitions.append(
(self.junk_registers[0], [r.name for r in self.prepare.junk_registers])
)
return bb.add_d(AutoPartition(self.prepare, partitions), **soqs)
def __str__(self) -> str:
- return 'Prep'
+ return f'BBPrepare[{self.prepare}]'
@bloq_example
diff --git a/qualtran/drawing/graphviz.py b/qualtran/drawing/graphviz.py
index b6e70050d..12835098e 100644
--- a/qualtran/drawing/graphviz.py
+++ b/qualtran/drawing/graphviz.py
@@ -402,6 +402,24 @@ def cxn_edge(self, left_id: str, right_id: str, cxn: Connection) -> pydot.Edge:
arrowsize=0.25,
)
+ def cxn_label(self, cxn: Connection) -> str:
+ import sympy
+
+ from qualtran.symbolics import is_symbolic
+
+ n = cxn.shape
+ if not is_symbolic(n):
+ return str(n)
+
+ label = sympy.printing.pretty(n)
+ label_lines = label.split('\n')
+ if len(label_lines) > 1:
+ return str(n)[:10] + " ..."
+
+ if len(label) > 15:
+ return label[:15] + " ..."
+ return label
+
class TypedGraphDrawer(PrettyGraphDrawer):
@staticmethod
diff --git a/qualtran/symbolics/simplification.py b/qualtran/symbolics/simplification.py
new file mode 100644
index 000000000..6c1cfb1ad
--- /dev/null
+++ b/qualtran/symbolics/simplification.py
@@ -0,0 +1,23 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+from qualtran.symbolics.types import SymbolicInt
+
+
+def extract_int(x: SymbolicInt) -> SymbolicInt:
+ """Extract a raw python int if the input is sympy.Integer, otherwise return as-is."""
+ try:
+ result = int(x)
+ return result
+ except TypeError:
+ return x