Add end to end qubitization example for 2D Hubbard model from Linear T complexity paper by tanujkhattar · Pull Request #224 · quantumlib/Qualtran

tanujkhattar · 2023-05-11T22:53:27Z

Implements SELECT and PREPARE for Hubbard model as described in Section V of https://arxiv.org/abs/1805.03662

Uses the newly added SELECT / PREPARE oracles to construct a Qubitization walk operator and perform Heisenberg limited phase estimation on the walk operator. Outputs resource counts for a 10x10 hubbard model grid in under ~1 second.

Fixes #31

…into hubbard_qubitization

…cirq-qubitization into hubbard_qubitization

fdmalone

Looks great up to a bit more exposition in the notebook. In particular I think it's a great place to compare to the linear T paper in a bit more depth. They provide formula and make approximations for the T complexity so it should be possible to include a few more figures and comment on where the missing T gates are.

cirq_qubitization/cirq_algos/hubbard_model.ipynb

fdmalone · 2023-05-16T04:43:13Z

cirq_qubitization/cirq_algos/hubbard_model.ipynb

+    "This follows section V. of the [Linear T Paper](https://arxiv.org/abs/1805.03662).\n",
+    "\n",
+    "The Hubbard model is a special case of the electronic structure Hamiltonian\n",
+    "restricted to spins on a planar grid.\n",


I'd be careful saying spins here, it's still a fermionic model and spins have some separate meaning in the model condensed matter world. Also it's not really rrestricted to live in a plane. The 1D and 3D Hubbard models are well defined models.

This was inspired from the following paragraph in the paper:

Can I reword to "The 2D Hubbard model is a special case of the electronic structure Hamiltonian
with fermions restricted on a planar grid." ? Can you suggest a better wording?

cirq_qubitization/cirq_algos/hubbard_model.ipynb

fdmalone · 2023-05-16T05:50:13Z

cirq_qubitization/cirq_algos/hubbard_model.ipynb

+    "- `x_dim`: the number of sites along the x axis.\n",
+    "- `y_dim`: the number of sites along the y axis.\n",
+    "- `t`: coefficient for XZX and YZY terms in the Hubbard model hamiltonian.\n",
+    "- `mu`: coefficeint for single body Z term and two-body ZZ terms in the Hubbard model hamiltonian.\n",


What is mu? I think you're calling mu = 4 t below, but it seems a bit unusual to me, normally one measures things in units of t, U = 4 t is just intermediate coupling.

Is there a better name for this coefficient than coefficient for Z and ZZ terms?

I set mu = 4 t below because the paper gives resource estimates for cases when mu = 4 t

The u in 57 is the same as the u in 56 right? When I saw mu I thought $\mu$ which also unfortunately crops up in the Hubbard model literature ( $\mu$ is the chemical potential). u is just the usual Hubbard U I think.

Should I rename mu to u ? There is already a capital U so I'm not sure if it'll cause more confusion.

I think it should just be u? They use capital U to mean something else in the paper.

cirq_qubitization/cirq_algos/hubbard_model.ipynb

…into hubbard_qubitization

…ginal paper

tanujkhattar

@fdmalone I've addressed all of your comments and also updated the notebook to show comparison of T-complexity costs obtained by our SELECT / PREPARE gates with the formulas given the paper. Specifically, the T-complexity for SELECT matches exactly (10*N + logN) and for PREPARE the paper only specifies an asymptotic cost of O(logN) whereas we demonstrate exact constant factors of 32 * logN in the paper.

I've also made the SVG diagrams nicer to include the T-complexity cost for each operation within the diagram. This is helpful to visualize the contribution of each operation in the decomposition.

This is ready for a re-review, PTAL!

…stimation

tanujkhattar · 2023-05-23T17:27:43Z

@fdmalone I also fixed the formula for calculating m_bits for heisenberg limited phase estimation (which I will move to a separate gate in a follow up PR).

Now, for a 20 x 20 2D Hubbard model grid, the end to end resource costs for heisenberg limited phase estimation using constants same as Table-IV of the paper gives the following resource costs:

T-count:   4.90109e+09
Rotations: 9.43787e+06
Cliffords: 2.31972e+10

Comparing to Table-IV, this is now much closer than the approximated number of 1.2e10. I claim that our number now is more accurate because the paper does a few upper bound approximations and this difference can be accounted for if we take just 2 extra bits of precisions when doing phase estimation.

fdmalone · 2023-05-23T17:32:55Z

cirq_qubitization/cirq_algos/hubbard_model.ipynb

+    "plt.xlabel('N')\n",
+    "plt.ylabel('T-costs')\n",
+    "plt.title('$SELECT_{Hubbard}$')\n",
+    "plt.plot(x, y, label='$10 * N + 14 * logN - 8$')\n",


I might just add marker="o" here or your favourite symbol. It's nice to see the specific points. But feel free to ignore.

fdmalone

LGTM % optional markers in plot, what are the [@t:28,...] bits in the controls?

tanujkhattar · 2023-05-23T17:35:36Z

what are the [@t:28,...] bits in the controls?

I updated the plotting code to also print the resource counts (number of T-gates and rotation gates) for each gate in the circuit. This is indicated by setting an additional flag when plotting the decomposition of an operation - display_gate_and_compilation(select, include_costs=True)

mpharrigan · 2023-05-23T17:43:40Z

cirq_qubitization/cirq_algos/hubbard_model.ipynb

+   "metadata": {
+    "cq.autogen": "_make_SelectHubbard.md"
+   },


so these cells were originally auto-generated using the jupyter autogen functionality in my PR. can you add their entries back in?

Do we have support for auto generating multiple cells (like for SELECT and PREPARE) using the autogen feature? I thought we were restricted to the simpler cases of generating 1 cell per notebook (eg: what was done in _make_SelectHubbard ) and thus I decided to remove tha autogen functionality.

cirq_qubitization/cirq_algos/hubbard_model.ipynb

mpharrigan · 2023-05-23T17:45:56Z

cirq_qubitization/cirq_algos/hubbard_model.ipynb

+    "plt.xlabel('N')\n",
+    "plt.ylabel('T-costs')\n",
+    "plt.title('$PREPARE_{Hubbard}$')\n",
+    "plt.plot(x, y_t, label='$O(logN)$ T-cost', marker=\"o\")\n",


I find these labels confusing. the first is the actual T cost, right? so why is it labeled with big-O?

Yes, because we don't have a simple formula for the exact T-cost since PrepareUniformSuperposition's cost depends on the factorization of the integer. Thus, it's upper bounded by O(logN) as given in the paper. I also plot an upper bounding constant.

cirq_qubitization/cirq_algos/hubbard_model.ipynb

cirq_qubitization/cirq_algos/phase_estimation_of_quantum_walk.py.ipynb

mpharrigan · 2023-05-23T17:48:55Z

cirq_qubitization/cirq_algos/hubbard_model.py

+
+    Args:
+        x_dim: the number of sites along the x axis.
+        y_dim: the number of sites along the y axis.


document control_val; should this be cv like elsewhere?

Yeah, but I want to punt the renaming of control_val to cvs for a later PR since it would also change the interface from Optional[int] to Tuple[int, ...].

tanujkhattar added 3 commits May 11, 2023 14:51

Add AdditionModN gate to cirq-algos

9f4e377

Fix pylint

3959e46

Add end to end qubitization example for 2D Hubbard model

63201a6

tanujkhattar requested review from NoureldinYosri and fdmalone May 11, 2023 22:53

tanujkhattar assigned NoureldinYosri, fdmalone and mpharrigan and unassigned NoureldinYosri May 11, 2023

Fix formatting and pylint errors

5963991

tanujkhattar mentioned this pull request May 11, 2023

SelectHubbard #107

Closed

tanujkhattar added 5 commits May 12, 2023 13:26

Add assertion and support pow for all integers

2809cc8

Add end to end qubitization example for 2D Hubbard model

5502783

Fix formatting and pylint errors

9eb19a1

Merge branch 'main' of https://github.com/quantumlib/cirq-qubitization …

aaf2bd0

…into hubbard_qubitization

Merge branch 'hubbard_qubitization' of https://github.com/quantumlib/…

0a7898d

…cirq-qubitization into hubbard_qubitization

fdmalone requested changes May 16, 2023

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tanujkhattar added 3 commits May 22, 2023 11:21

Merge branch 'main' of https://github.com/quantumlib/cirq-qubitization …

8050f94

…into hubbard_qubitization

Merge branch 'main' of https://github.com/quantumlib/cirq-qubitization …

d6c181d

…into hubbard_qubitization

Address comments and update notebook to show comparision with the ori…

ee0004b

…ginal paper

tanujkhattar commented May 23, 2023

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tanujkhattar added 2 commits May 23, 2023 03:14

Fix circular import and pylint

4017f23

Fix typo in hubbard model notebook and fix m_bits formula for phase e…

a90837a

…stimation

fdmalone reviewed May 23, 2023

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fdmalone approved these changes May 23, 2023

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Add marker to plots

26ef735

tanujkhattar enabled auto-merge (squash) May 23, 2023 17:37

mpharrigan reviewed May 23, 2023

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tanujkhattar disabled auto-merge May 23, 2023 17:44

mpharrigan reviewed May 23, 2023

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mpharrigan reviewed May 23, 2023

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Address Matts comments

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tanujkhattar merged commit 65bc8ec into main May 23, 2023

mpharrigan deleted the hubbard_qubitization branch November 20, 2023 20:02

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