Add bloq for Binary Polynomial Multiplication

dev_tools/qualtran_dev_tools/notebook_specs.py

@@ -576,6 +576,8 @@
         bloq_specs=[
             qualtran.bloqs.gf_arithmetic.gf2_multiplication._GF2_MULTIPLICATION_DOC,
             qualtran.bloqs.gf_arithmetic.gf2_multiplication._MULTIPLY_BY_CONSTANT_MOD_DOC,
+            qualtran.bloqs.gf_arithmetic.gf2_multiplication._MULTIPLY_POLY_BY_ONE_PLUS_XK_DOC,
+            qualtran.bloqs.gf_arithmetic.gf2_multiplication._BINARY_POLYNOMIAL_MULTIPLICATION_DOC,
         ],
     ),
     NotebookSpecV2(

qualtran/bloqs/gf_arithmetic/__init__.py

@@ -16,7 +16,9 @@
 from qualtran.bloqs.gf_arithmetic.gf2_addition import GF2Addition
 from qualtran.bloqs.gf_arithmetic.gf2_inverse import GF2Inverse
 from qualtran.bloqs.gf_arithmetic.gf2_multiplication import (
+    BinaryPolynomialMultiplication,
     GF2Multiplication,
     GF2MultiplyByConstantMod,
+    MultiplyPolyByOnePlusXk,
 )
 from qualtran.bloqs.gf_arithmetic.gf2_square import GF2Square

qualtran/bloqs/gf_arithmetic/gf2_multiplication.ipynb

@@ -289,16 +289,257 @@
     "show_call_graph(gf2_multiply_by_constant_modulu_g)\n",
     "show_counts_sigma(gf2_multiply_by_constant_modulu_sigma)"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0b276213",
+   "metadata": {
+    "cq.autogen": "MultiplyPolyByOnePlusXk.bloq_doc.md"
+   },
+   "source": [
+    "## `MultiplyPolyByOnePlusXk`\n",
+    "Out of place multiplication of $(1 + x^k) fg$\n",
+    "\n",
+    "Applies the transformation\n",
+    "$$\n",
+    "\\ket{f}\\ket{g}\\ket{h} \\rightarrow \\ket{f}{\\ket{g}}\\ket{h \\oplus (1+x^k)fg}\n",
+    "$$\n",
+    "\n",
+    "Note: While this construction follows Algorithm2 of https://arxiv.org/abs/1910.02849v2,\n",
+    "it has a slight modification. Namely that the original construction doesn't work in\n",
+    "some cases where $k < n$. However reversing the order of the first set of CNOTs (line 2)\n",
+    "makes the construction work for all $k \\leq n+1$.\n",
+    "\n",
+    "#### Parameters\n",
+    " - `n`: The degree of the polynomial ($2^n$ is the size of the galois field).\n",
+    " - `k`: An integer specifing the shift $1 + x^k$ (or $1 + 2^k$ for galois fields.) \n",
+    "\n",
+    "#### Registers\n",
+    " - `f`: The first polynomial.\n",
+    " - `g`: The second polyonmial.\n",
+    " - `h`: The target polynomial. \n",
+    "\n",
+    "#### References\n",
+    " - [Space-efficient quantum multiplication of polynomials for binary finite fields with     sub-quadratic Toffoli gate count](https://arxiv.org/abs/1910.02849v2). Algorithm 2\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9949a24e",
+   "metadata": {
+    "cq.autogen": "MultiplyPolyByOnePlusXk.bloq_doc.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.bloqs.gf_arithmetic import MultiplyPolyByOnePlusXk"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dd7c9a74",
+   "metadata": {
+    "cq.autogen": "MultiplyPolyByOnePlusXk.example_instances.md"
+   },
+   "source": [
+    "### Example Instances"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ad918c9f",
+   "metadata": {
+    "cq.autogen": "MultiplyPolyByOnePlusXk.multiplypolybyoneplusxk"
+   },
+   "outputs": [],
+   "source": [
+    "n = 5\n",
+    "k = 3\n",
+    "multiplypolybyoneplusxk = MultiplyPolyByOnePlusXk(n, k)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "aa939469",
+   "metadata": {
+    "cq.autogen": "MultiplyPolyByOnePlusXk.graphical_signature.md"
+   },
+   "source": [
+    "#### Graphical Signature"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "648d128f",
+   "metadata": {
+    "cq.autogen": "MultiplyPolyByOnePlusXk.graphical_signature.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.drawing import show_bloqs\n",
+    "show_bloqs([multiplypolybyoneplusxk],\n",
+    "           ['`multiplypolybyoneplusxk`'])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4bb8dcef",
+   "metadata": {
+    "cq.autogen": "MultiplyPolyByOnePlusXk.call_graph.md"
+   },
+   "source": [
+    "### Call Graph"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "0890198e",
+   "metadata": {
+    "cq.autogen": "MultiplyPolyByOnePlusXk.call_graph.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.resource_counting.generalizers import ignore_split_join\n",
+    "multiplypolybyoneplusxk_g, multiplypolybyoneplusxk_sigma = multiplypolybyoneplusxk.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
+    "show_call_graph(multiplypolybyoneplusxk_g)\n",
+    "show_counts_sigma(multiplypolybyoneplusxk_sigma)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9d9d1540",
+   "metadata": {
+    "cq.autogen": "BinaryPolynomialMultiplication.bloq_doc.md"
+   },
+   "source": [
+    "## `BinaryPolynomialMultiplication`\n",
+    "Out of place multiplication of binary polynomial multiplication.\n",
+    "\n",
+    "Applies the transformation\n",
+    "$$\n",
+    "\\ket{f}\\ket{g}\\ket{h} \\rightarrow \\ket{f}{\\ket{g}}\\ket{h \\oplus fg}\n",
+    "$$\n",
+    "\n",
+    "The toffoli cost of this construction is $n^{\\log_2{3}}$, while CNOT count is\n",
+    "upper bounded by $(10 + \\frac{1}{3}) n^{\\log_2{3}}$.\n",
+    "\n",
+    "#### Parameters\n",
+    " - `n`: The degree of the polynomial ($2^n$ is the size of the galois field). \n",
+    "\n",
+    "#### Registers\n",
+    " - `f`: The first polynomial.\n",
+    " - `g`: The second polyonmial.\n",
+    " - `h`: The target polynomial. \n",
+    "\n",
+    "#### References\n",
+    " - [Space-efficient quantum multiplication of polynomials for binary finite fields with     sub-quadratic Toffoli gate count](https://arxiv.org/abs/1910.02849v2). Algorithm 3\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1ba3a057",
+   "metadata": {
+    "cq.autogen": "BinaryPolynomialMultiplication.bloq_doc.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.bloqs.gf_arithmetic import BinaryPolynomialMultiplication"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "296d193b",
+   "metadata": {
+    "cq.autogen": "BinaryPolynomialMultiplication.example_instances.md"
+   },
+   "source": [
+    "### Example Instances"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "907fcd25",
+   "metadata": {
+    "cq.autogen": "BinaryPolynomialMultiplication.binarypolynomialmultiplication"
+   },
+   "outputs": [],
+   "source": [
+    "n = 5\n",
+    "binarypolynomialmultiplication = BinaryPolynomialMultiplication(n)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a100a193",
+   "metadata": {
+    "cq.autogen": "BinaryPolynomialMultiplication.graphical_signature.md"
+   },
+   "source": [
+    "#### Graphical Signature"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "aad80309",
+   "metadata": {
+    "cq.autogen": "BinaryPolynomialMultiplication.graphical_signature.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.drawing import show_bloqs\n",
+    "show_bloqs([binarypolynomialmultiplication],\n",
+    "           ['`binarypolynomialmultiplication`'])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c1d23614",
+   "metadata": {
+    "cq.autogen": "BinaryPolynomialMultiplication.call_graph.md"
+   },
+   "source": [
+    "### Call Graph"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8dc799ef",
+   "metadata": {
+    "cq.autogen": "BinaryPolynomialMultiplication.call_graph.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.resource_counting.generalizers import ignore_split_join\n",
+    "binarypolynomialmultiplication_g, binarypolynomialmultiplication_sigma = binarypolynomialmultiplication.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
+    "show_call_graph(binarypolynomialmultiplication_g)\n",
+    "show_counts_sigma(binarypolynomialmultiplication_sigma)"
+   ]
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
   "language_info": {
-   "name": "python"
+   "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,