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arxiv: 2404.19497 · v4 · submitted 2024-04-30 · 🪐 quant-ph

Light Cone Cancellation for Variational Quantum Eigensolver in Solving Noisy Max-Cut

Xinwei Lee , Xinjian Yan , Ningyi Xie , Yoshiyuki Saito , Leo Kurosawa , Nobuyoshi Asai , Dongsheng Cai , Hoong Chuin LAU This is my paper

Pith reviewed 2026-05-24 01:51 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Variational Quantum EigensolverLight Cone CancellationMax-Cutquantum noise mitigationapproximation ratiotwo-local ansatzquantum circuit decomposition
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The pith

Light cone cancellation applied to VQE raises approximation ratios on noisy Max-Cut instances up to 100 qubits.

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

The paper tests light cone cancellation inside a variational quantum eigensolver for the Max-Cut problem. The cancellation step drops gates that do not contribute to the expectation value of any local observable, which splits the original circuit into several smaller subcircuits and lowers the total gate count. When the resulting LCC-VQE circuits are executed on simulated noisy hardware modeled after 7-qubit and 27-qubit devices, they produce higher approximation ratios than identical circuits run without cancellation. The improvement appears for single-layer two-local ansatzes; deeper layers were also examined but performed worse. The same circuits are compared with the classical Goemans-Williamson algorithm under noiseless conditions.

Core claim

Light cone cancellation applied to a single-layer two-local ansatz decomposes each variational circuit into multiple subcircuits that use fewer qubits and fewer gates. On fake noisy backends the reduced circuits return higher approximation ratios for Max-Cut instances up to 100 qubits than the unreduced circuits, which the authors interpret as evidence that device noise is mitigated. Multi-layer ansatzes were tested but the single-layer version remained superior under the same noise model.

What carries the argument

Light Cone Cancellation (LCC), the procedure that removes gates whose removal does not change the expectation value of any local observable, thereby enabling decomposition into smaller subcircuits.

If this is right

  • Max-Cut problems larger than the available qubit count can be solved by evaluating only the smaller subcircuits.
  • Fewer gates per subcircuit reduce the total error accumulated from hardware noise.
  • The single-layer two-local ansatz combined with LCC outperforms multi-layer versions on the tested noisy simulators.
  • The method produces approximation ratios that can be compared directly with the Goemans-Williamson classical bound under noiseless conditions.

Where Pith is reading between the lines

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

  • The same cancellation technique could be applied to other variational algorithms whose cost functions depend on local observables.
  • Subcircuit decomposition may enable parallel execution across multiple small quantum processors.
  • Combining LCC with additional error-suppression methods could further enlarge the size of solvable instances.

Load-bearing premise

The cancellation step removes only gates that truly have no effect on the measured local observable, so the smaller subcircuits still compute exactly the same expectation values as the original circuit.

What would settle it

If the same Max-Cut instances run on real quantum hardware show no improvement or a reversal in approximation ratio when LCC is used versus when it is not used, the claimed noise-mitigation benefit would be falsified.

Figures

Figures reproduced from arXiv: 2404.19497 by Dongsheng Cai, Hoong Chuin LAU, Leo Kurosawa, Ningyi Xie, Nobuyoshi Asai, Xinjian Yan, Xinwei Lee, Yoshiyuki Saito.

Figure 1
Figure 1. Figure 1: FIG. 1: Two-local ansatz used in the simulations in our work. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (a) The light cone cancellation (LCC) in a single layer two-local ansatz. The expectation function [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Overall workflow of the LCC in two-local ansatz. The expectation function [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Percentage of AR [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The entanglement map after LCC when the number of [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Comparison of the approximation ratio (AR) for the VQE solved with a 7-qubit fake backend [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Comparison of the AR for the VQE with LCC and without [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: (a) Comparison of the AR for LCC-VQE and GW algorithm on 100-vertex [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Coupling map of [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Coupling map of [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
read the original abstract

Variational Quantum Eigensolver (VQE) is a quantum-classical hybrid algorithm used to estimate the ground energy of a given Hamiltonian. It consists of a parameterized quantum circuit, which the parameters are optimized using a classical optimizer. With the increasing need in solving large-scale problems in real-world applications, solving those large problems with fewer qubits and fewer gates becomes essential, so that we reduce the simulation difficulty and mitigate the effect of noise in real quantum hardware. In this study, we applied the Light Cone Cancellation (LCC) method to reduce the number of qubits and gates required in a two-local ansatz. LCC removes redundant gates that are not required in the calculation of the expectation value for a local observable. This leads to two consequences: 1) the quantum circuit used to create the trial wavefunction of VQE can be broken down into multiple quantum subcircuits with fewer qubits, enabling large-scale problems to be solved without actually simulating the entire circuit; and 2) reduced number of quantum gates in the circuit leads to the noise mitigation in quantum hardware. The main purpose of this work is to demonstrate the effectiveness of this method (called the LCC-VQE) in mitigating the device noise when solving the Max-Cut problem up to 100 qubits, using simulations on small (7-qubit and 27-qubit) fake noisy backends. Employing a single-layer two-local ansatz circuit architecture, the reuslts show that LCC-VQE yields higher approximation ratios than those cases without LCC, implying that the effect of noise is mitigated when LCC is applied. An analysis of more than one layer of two-local ansatz is also performed, but empirical results show that the single-layer ansatz still performs the best among them. We also compare LCC-VQE under noiseless conditions with the Goemans-Williamson algorithm.

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

3 major / 2 minor

Summary. The paper proposes Light Cone Cancellation (LCC) for VQE on Max-Cut instances, using a single-layer two-local ansatz. LCC decomposes the circuit into smaller subcircuits by canceling gates outside the causal light cone of each local ZZ observable, reducing qubit and gate counts. Simulations on 7- and 27-qubit fake noisy backends for problems up to 100 qubits report higher approximation ratios with LCC-VQE than without; single-layer ansatz outperforms multi-layer variants, and noiseless LCC-VQE is compared to the Goemans-Williamson algorithm.

Significance. If the empirical noise-mitigation claim holds under proper statistical controls, the method offers a practical route to scale VQE for combinatorial problems on NISQ hardware by exploiting the locality of the Max-Cut Hamiltonian. The light-cone reduction is a standard and parameter-free consequence of the two-local ansatz and observable structure, providing a clear theoretical basis for the gate-count savings.

major comments (3)
  1. [§4, Figure 3] §4 (Results), Figure 3 and associated text: approximation ratios for LCC-VQE versus standard VQE are reported without error bars, number of independent runs, or statistical significance tests; this directly undermines the central claim that LCC mitigates noise, as the observed differences cannot be assessed for robustness.
  2. [§3.2] §3.2 (Methods): the classical optimizer (type, learning rate, iteration count, convergence tolerance) and exact gate counts before/after LCC are not specified; these details are load-bearing for reproducing the VQE optimization trajectories and for quantifying the noise reduction attributed to fewer gates.
  3. [§4.3] §4.3 (multi-layer analysis): the statement that the single-layer ansatz performs best lacks quantitative metrics (e.g., final approximation ratios or variance across layers) and a clear description of how deeper circuits were optimized under the same noise model, weakening the architectural recommendation.
minor comments (2)
  1. [Abstract] Abstract: typo 'reuslts' should be 'results'.
  2. [§2] Notation for the reduced subcircuits and the precise definition of the light-cone cutoff could be clarified with a small diagram or explicit equation in §2.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which highlight important aspects for improving the clarity and rigor of our empirical claims. We address each major comment below and will revise the manuscript to incorporate the suggested enhancements.

read point-by-point responses

  1. Referee: [§4, Figure 3] §4 (Results), Figure 3 and associated text: approximation ratios for LCC-VQE versus standard VQE are reported without error bars, number of independent runs, or statistical significance tests; this directly undermines the central claim that LCC mitigates noise, as the observed differences cannot be assessed for robustness.

    Authors: We agree that the lack of error bars, run counts, and statistical tests weakens the ability to evaluate the robustness of the noise-mitigation results. In the revised version, we will rerun the simulations with multiple independent optimizations (at least 10 runs per problem instance) under the same noise models, report mean approximation ratios with standard error bars, and include p-values from paired t-tests comparing LCC-VQE and standard VQE to quantify significance. revision: yes

  2. Referee: [§3.2] §3.2 (Methods): the classical optimizer (type, learning rate, iteration count, convergence tolerance) and exact gate counts before/after LCC are not specified; these details are load-bearing for reproducing the VQE optimization trajectories and for quantifying the noise reduction attributed to fewer gates.

    Authors: We acknowledge these omissions hinder reproducibility. The revised Methods section will explicitly state the optimizer (COBYLA), its parameters (e.g., maxiter=200, tol=1e-6), and provide a table of exact gate counts (CNOT and single-qubit) before and after LCC for representative 7-, 27-, and 100-qubit instances, along with the resulting circuit depths. revision: yes

  3. Referee: [§4.3] §4.3 (multi-layer analysis): the statement that the single-layer ansatz performs best lacks quantitative metrics (e.g., final approximation ratios or variance across layers) and a clear description of how deeper circuits were optimized under the same noise model, weakening the architectural recommendation.

    Authors: We will expand §4.3 with a table reporting mean approximation ratios and variances for 1-, 2-, and 3-layer ansatze across the test instances. The text will clarify that all layer depths were optimized using identical hyperparameters, the same fake backend noise models, and the same number of shots to ensure fair comparison. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's central claim rests on direct numerical simulations comparing approximation ratios of LCC-VQE versus standard VQE on fake noisy backends for Max-Cut instances up to 100 qubits, using an explicit single-layer two-local ansatz. The LCC step is justified by standard causal light-cone arguments on local ZZ observables, which leave the ideal expectation value unchanged while reducing gate count; this is not derived from any fitted parameter, self-citation chain, or ansatz smuggled in via prior work by the same authors. No equations reduce a prediction to its input by construction, and the noiseless comparison to Goemans-Williamson is an external benchmark. The derivation chain is therefore self-contained and externally falsifiable via the reported circuit simulations.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract relies on standard definitions of VQE, two-local ansatz, and light-cone cancellation from prior literature; no new free parameters, axioms, or invented entities are introduced.

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Forward citations

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