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arxiv: 2501.04776 · v2 · submitted 2025-01-08 · 🪐 quant-ph

IQPopt: Fast optimization of instantaneous quantum polynomial circuits in JAX

Erik Armengol , Joseph Bowles This is my paper

Pith reviewed 2026-05-23 05:33 UTC · model grok-4.3

classification 🪐 quant-ph
keywords IQP circuitsclassical optimizationPauli-Z observablesJAXquantum generative modelsmaximum mean discrepancyclassical simulationinstantaneous quantum polynomial
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The pith

Large instantaneous quantum polynomial circuits can be optimized on classical hardware when objectives depend on Pauli-Z observables.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces IQPopt, a JAX-based package that optimizes large-scale instantaneous quantum polynomial circuits on classical computers. It does so by using an efficient classical simulation algorithm to estimate expectation values whenever the objective function can be expressed in terms of Pauli-Z type observables. A sympathetic reader would care because sampling from these circuits is widely believed to be classically hard, so the method lets users identify strong circuit instances before committing them to quantum hardware. The package also includes a dedicated module for training and evaluating quantum generative models with maximum mean discrepancy and supports acceleration on GPUs.

Core claim

IQPopt exploits an efficient classical simulation algorithm for expectation value estimation of Pauli-Z observables in IQP circuits, enabling optimization of circuits with thousands of qubits and millions of gates on classical hardware provided the objective function has an efficient description in terms of such observables. This supplies a practical route to locate powerful circuit instances prior to deployment and sampling on quantum hardware where computational advantages may exist.

What carries the argument

Efficient classical simulation algorithm for Pauli-Z expectation values in IQP circuits, combined with JAX automatic differentiation.

If this is right

  • Optimized circuits can be transferred to quantum hardware for sampling where classical hardness may confer advantage.
  • The MMD module permits training and evaluation of quantum generative models on the same classical infrastructure.
  • Hardware accelerators such as GPUs can further speed up the optimization process.
  • Users can tune million-gate circuits classically before quantum execution.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same simulation technique could be adapted to other circuit families that admit efficient Pauli observable evaluation.
  • This classical preprocessor could help benchmark claims of quantum advantage by supplying high-quality starting points.
  • Extensions to additional observable classes would broaden the range of objective functions that become classically tractable.

Load-bearing premise

An efficient classical simulation algorithm exists for estimating expectation values of Pauli-Z observables in IQP circuits at the scale of thousands of qubits.

What would settle it

A demonstration that simulation time or memory for Pauli-Z expectation values grows exponentially with qubit number in some IQP circuit, or that the optimizer cannot reach claimed scale within feasible classical resources.

Figures

Figures reproduced from arXiv: 2501.04776 by Erik Armengol, Joseph Bowles.

Figure 1
Figure 1. Figure 1: Overview of IQP circuit optimization in IQPopt ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (left): An example code block that defines a 300 qubit circuit with 45150 parameters [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The computational graph computed by IQPopt. The matrices [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Diagram of the structure of the package. While [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Runtimes for the batch estimation of 10000 randomly chosen observables, for different [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (left) Execution time for the benchmark of Sec. [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Runtime to estimate the squared maximum mean discrepancy of Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
read the original abstract

IQPopt is a software package designed to optimize large-scale instantaneous quantum polynomial circuits on classical hardware. By exploiting an efficient classical simulation algorithm for expectation value estimation, circuits with thousands of qubits and millions of gates can be optimized, provided the relevant objective function has an efficient description in terms of Pauli-Z type observables. Since sampling from instantaneous quantum polynomial circuits is widely believed to be hard for classical computers, this provides a method to identify powerful circuit instances before deployment and sampling on quantum hardware, where computational advantages may exist. The package leverages automatic differentiation in JAX, can be accelerated with access to hardware accelerators such as graphics processing units, and contains a dedicated module that can be used to train and evaluate quantum generative models via the maximum mean discrepancy.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces IQPopt, a JAX-based software package for optimizing large-scale instantaneous quantum polynomial (IQP) circuits on classical hardware. It exploits an efficient classical simulation algorithm for estimating expectation values of Pauli-Z observables to optimize circuits with thousands of qubits and millions of gates when the objective function admits an efficient description as a linear combination of such observables. The package supports automatic differentiation, GPU acceleration, and includes a dedicated module for training and evaluating quantum generative models via maximum mean discrepancy.

Significance. If the claimed efficient classical simulation for Pauli-Z expectations holds at the stated scales, the work provides a practical tool for pre-optimizing IQP circuit instances prior to quantum sampling, where computational advantages may appear. The JAX implementation with autodiff and hardware acceleration is a useful engineering contribution, and the MMD module for generative models adds direct applicability to quantum machine learning tasks.

major comments (2)
  1. [Abstract] Abstract: the claim that circuits with thousands of qubits and millions of gates can be optimized rests on the existence of a poly(n, gates) classical algorithm for Pauli-Z expectation estimation, yet no derivation, complexity bound, error analysis, or scaling verification is supplied.
  2. [Simulation method (implied in abstract and package description)] The assertion of an efficient path for Pauli-Z observables (distinct from #P-hard sampling) is load-bearing, but the text provides no explicit gate-structure restrictions, handling of growing observable support, or benchmarks confirming sub-exponential scaling at n~1000 with 10^6 gates.
minor comments (1)
  1. [Package description] Specify the precise mapping from objective functions to Pauli-Z observables and any restrictions on the diagonal phase gates to support reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the need for greater technical detail on the simulation method. We address each major comment below and will revise the manuscript to incorporate the requested clarifications, derivations, and benchmarks.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that circuits with thousands of qubits and millions of gates can be optimized rests on the existence of a poly(n, gates) classical algorithm for Pauli-Z expectation estimation, yet no derivation, complexity bound, error analysis, or scaling verification is supplied.

    Authors: We agree that the abstract's claim requires supporting technical detail in the main text. The underlying simulation exploits the commuting diagonal structure of IQP circuits to reduce Pauli-Z expectation estimation to a classical computation whose cost is polynomial in n and the number of gates when the objective is a linear combination of Pauli-Z observables with bounded support. In the revision we will add an explicit derivation of the algorithm, its complexity bound, error analysis for the estimator, and scaling benchmarks that confirm the claimed regime. revision: yes

  2. Referee: [Simulation method (implied in abstract and package description)] The assertion of an efficient path for Pauli-Z observables (distinct from #P-hard sampling) is load-bearing, but the text provides no explicit gate-structure restrictions, handling of growing observable support, or benchmarks confirming sub-exponential scaling at n~1000 with 10^6 gates.

    Authors: The method applies specifically to IQP circuits (Hadamard layers sandwiching commuting diagonal gates) and to objectives whose Pauli-Z decomposition has support that does not grow exponentially with circuit size; under these restrictions the observable support remains tractable and the cost stays polynomial. We will expand the manuscript to state these restrictions explicitly, describe how growing support is avoided or truncated, and add numerical scaling results up to the stated sizes. revision: yes

Circularity Check

0 steps flagged

No circularity; software package implements stated simulation technique

full rationale

The manuscript presents a JAX-based optimization tool for IQP circuits that exploits an efficient classical algorithm for Pauli-Z expectation values when the objective admits an efficient description in those observables. No derivation of the simulation algorithm itself is claimed, no parameters are fitted to data and then relabeled as predictions, and no self-citation chain is invoked to justify a uniqueness result or ansatz. The work is therefore a self-contained implementation description whose central capability rests on the pre-existing simulation method rather than on any internal reduction to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The paper introduces no new free parameters, axioms, or invented entities; it is an implementation of known classical simulation techniques for a restricted class of quantum circuits.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Parity Supervision as a Driver of Generalization in Quantum Generative Modeling

    quant-ph 2026-05 unverdicted novelty 5.0

    Parity supervision improves exact KL fit and recovery of unseen high-value states in IQP Born machines beyond MSE training or max-entropy controls via parity-moment evidence transfer.

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