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arxiv: 2604.26477 · v2 · pith:DGBTVKXTnew · submitted 2026-04-29 · 🪐 quant-ph

Multi-Objective Optimization by Quantum-Annealing-Inspired Algorithms

Xian-Zhe Tao , Pavel Mosharev , Man-Hong Yung This is my paper

Pith reviewed 2026-05-21 09:36 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum annealingmulti-objective optimizationMaxCutquantum-inspired algorithmscombinatorial optimizationGPU accelerationclassical solversruntime overhead
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The pith

GPU-based quantum-annealing-inspired algorithms outperform previous quantum processors and top classical solvers on MO-MaxCut problems when full runtimes are measured.

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

This paper re-examines multi-objective MaxCut optimization benchmarks that earlier studies had used to compare quantum processors against classical methods. Those prior comparisons left out the substantial time required for preparing problem data and handling results after sampling. The authors instead test GPU implementations of quantum-annealing-inspired algorithms that produce probabilistic candidate solutions in the same manner as quantum hardware. These classical algorithms generate usable samples roughly two orders of magnitude faster than the quantum processors previously reported. When complete end-to-end times are tallied, the inspired methods also finish ahead of industry-leading classical solvers, making them the fastest option among all approaches evaluated for these instances.

Core claim

The paper shows that GPU-based quantum-annealing-inspired algorithms sample candidate solutions for MO-MaxCut instances approximately two orders of magnitude faster than the quantum processors examined in earlier work. Once pre- and post-processing overheads are included to obtain true end-to-end runtime, these algorithms also surpass the performance of leading classical solvers and thereby rank as the strongest performers across the quantum and classical methods tested on the same benchmark suite.

What carries the argument

GPU-based quantum-annealing-inspired algorithms that generate probabilistic samples analogous to quantum processors, used here as an overhead-matched classical baseline for direct speed and runtime comparisons.

If this is right

  • Future claims of quantum advantage in combinatorial optimization must incorporate full pre- and post-processing overheads to be considered complete.
  • QAIAs establish a higher performance threshold that quantum hardware must exceed on these problems.
  • Classical sampling methods accelerated by GPUs can serve as strong proxies for quantum behavior in benchmark comparisons.
  • MO-MaxCut instances favor these inspired algorithms over both quantum devices and other classical solvers when runtime is measured end-to-end.

Where Pith is reading between the lines

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

  • If the speed advantage holds for larger problem sizes, quantum processors would require substantial reductions in overhead to become competitive.
  • The same overhead-accounting approach could be applied to other optimization problems where quantum advantage has been suggested.
  • Hybrid systems that combine QAIAs with limited quantum calls might further improve performance on related tasks.
  • This work underscores the need for standardized full-runtime protocols when benchmarking quantum and classical solvers.

Load-bearing premise

The results rest on the premise that prior quantum studies omitted pre- and post-processing times and that the chosen GPU implementations introduce no hidden speed advantages beyond those available to any careful classical re-implementation.

What would settle it

A side-by-side measurement on the same MO-MaxCut instances that includes every pre- and post-processing step and shows quantum processors achieving faster sampling or shorter total runtime than the QAIAs would directly challenge the superiority claim.

Figures

Figures reproduced from arXiv: 2604.26477 by Man-Hong Yung, Pavel Mosharev, Xian-Zhe Tao.

Figure 1
Figure 1. Figure 1: Convergence of different algorithms towards the Pareto front. The y-axis shows the Hypervolume view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of sampling time with full Pareto front reconstruction time. The y-axis shows the Hypervol view at source ↗
Figure 3
Figure 3. Figure 3: a) Convergence to optimal hypervolume for original and noisy SB. b) Distribution of numbers of samples needed by NI-SB to discover whole Pareto set of the 3-objective problem. Values for Quantum Annealing and QAOA according to [22] and [19]. c) Illustration of the Pareto front for two-objective problem with correlation coefficient between the two objectives equal approximately to −0.92. lation size is set … view at source ↗
Figure 4
Figure 4. Figure 4: Left: Das-Dennis simplex lattice points compared to random Dirichlet distribution for 3-objective problem. Middle: Hypervolume difference for solutions found by exact solver at each number of fixed weight vectors. Right: Number of Pareto-optimal solutions found by exact solver at each number of fixed weight vectors. 13 view at source ↗
Figure 5
Figure 5. Figure 5: Total sample size required to reach optimal hypervolume, depending on different amplitude of noise view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of SimCIM and NI-SB. The y-axis shows the Hypervolume difference ( view at source ↗
read the original abstract

Combinatorial optimization is widely regarded as a primary application for near-term quantum processors, although a definitive demonstration of the practical quantum advantage remains elusive. Recent studies have reported that both gate-based quantum circuits and quantum annealers can outperform state-of-the-art classical heuristics on multi-objective optimization (MO-MaxCut) problems. However, these studies did not fully account for the substantial pre- and post-processing overheads intrinsic to quantum solvers, leading to incomplete comparisons between quantum and classical approaches. In this work, we re-examine the same benchmark suite using GPU-based quantum-annealing-inspired algorithms (QAIAs), which, analogously to quantum processors, generate probabilistic samples and thus serve as formidable classical contenders. Our results show that QAIAs can sample candidate solutions approximately two orders of magnitude faster than previously studied quantum processors. In terms of end-to-end runtime, QAIAs also surpass industry-leading classical solvers, thereby establishing themselves as the superior performers among the quantum and classical solvers evaluated thus far for the MO-MaxCut instances.

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 / 1 minor

Summary. The manuscript re-examines the MO-MaxCut benchmark suite previously studied with quantum processors. It introduces GPU-based quantum-annealing-inspired algorithms (QAIAs) as classical probabilistic samplers that properly incorporate pre- and post-processing overheads. The central claim is that these QAIAs sample solutions approximately two orders of magnitude faster than the quantum processors and outperform industry-leading classical solvers in end-to-end runtime, positioning QAIAs as the best performers among the evaluated solvers.

Significance. If the runtime comparisons prove robust under identical instance sets, equivalent end-to-end timing definitions, and fully disclosed implementation details, the work would supply a strong, reproducible classical baseline that challenges claims of practical quantum advantage for near-term devices on this multi-objective optimization task. The explicit focus on overhead accounting and the use of GPU-accelerated classical analogs constitute a constructive contribution to the ongoing quantum-vs-classical benchmarking discussion.

major comments (3)
  1. [Abstract and Results] Abstract and Results section: the reported ~100x sampling speedup and end-to-end superiority rest on runtime measurements whose statistical reliability is not yet demonstrated; without the number of independent trials, standard deviations, or explicit handling of instance selection, it remains possible that the gap is sensitive to post-hoc choices or variance in the experimental setup.
  2. [Methods] Methods section: the claim that QAIAs constitute a fair, overhead-matched classical baseline requires a precise description of how pre- and post-processing times are measured and included for both the QAIAs and the re-examined quantum processors; any undisclosed implementation advantages (e.g., optimized GPU kernels or selective instance filtering) would undermine the direct comparison.
  3. [Results] Results section: because QAIAs hyperparameters are listed as free parameters, the manuscript should report the tuning protocol and whether the same hyperparameter search budget was afforded to the classical industry solvers; otherwise the performance edge may be partly attributable to unequal optimization effort.
minor comments (1)
  1. [Notation] Notation for runtime components (sampling time vs. total time) should be defined consistently in a single table or equation to avoid reader confusion when comparing figures.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We have carefully considered each major comment and provide point-by-point responses below. Where appropriate, we have revised the manuscript to address the concerns raised, enhancing the clarity and robustness of our claims.

read point-by-point responses

  1. Referee: [Abstract and Results] Abstract and Results section: the reported ~100x sampling speedup and end-to-end superiority rest on runtime measurements whose statistical reliability is not yet demonstrated; without the number of independent trials, standard deviations, or explicit handling of instance selection, it remains possible that the gap is sensitive to post-hoc choices or variance in the experimental setup.

    Authors: We appreciate this observation regarding the need for statistical details. In the revised manuscript, we now explicitly state that all runtime measurements were averaged over 20 independent trials per instance, with standard deviations reported in the supplementary material. Instance selection followed the exact protocol from the original MO-MaxCut benchmark suite without any post-hoc filtering. The observed speedups remain consistent across these trials, with relative standard deviations below 15%. revision: yes

  2. Referee: [Methods] Methods section: the claim that QAIAs constitute a fair, overhead-matched classical baseline requires a precise description of how pre- and post-processing times are measured and included for both the QAIAs and the re-examined quantum processors; any undisclosed implementation advantages (e.g., optimized GPU kernels or selective instance filtering) would undermine the direct comparison.

    Authors: We agree that detailed accounting is essential. The revised Methods section now includes a step-by-step breakdown of time measurements: for quantum processors, we incorporated all pre- and post-processing overheads as documented in the referenced prior works; for QAIAs, we measured wall-clock times including data transfer to/from GPU, kernel execution, and result post-processing using standard CUDA timing APIs. No optimized custom kernels beyond standard libraries were used, and all instances were processed without selective filtering. revision: yes

  3. Referee: [Results] Results section: because QAIAs hyperparameters are listed as free parameters, the manuscript should report the tuning protocol and whether the same hyperparameter search budget was afforded to the classical industry solvers; otherwise the performance edge may be partly attributable to unequal optimization effort.

    Authors: To address this, we have added a new subsection in the revised manuscript detailing the hyperparameter tuning protocol for QAIAs, which consisted of a systematic grid search over key parameters (e.g., annealing schedule, noise levels) with a total computational budget of approximately 100 CPU-hours. For the industry solvers, we used the default or best-reported hyperparameters from their respective publications, which typically involved similar or greater tuning efforts by their developers. We believe this provides a fair comparison, but we note that exhaustive tuning for all solvers would be computationally prohibitive. revision: partial

Circularity Check

0 steps flagged

No significant circularity; empirical runtime study is self-contained

full rationale

The paper reports direct empirical timing measurements of GPU-implemented QAIAs on the MO-MaxCut benchmark suite, including pre- and post-processing overheads, and compares these to previously published quantum and classical solver results. No equations, fitted parameters, or derivation steps are present that reduce by construction to the paper's own inputs or self-citations. The central performance claims rest on reproducible runtime data rather than any self-referential or ansatz-based chain, rendering the analysis independent and non-circular.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 0 invented entities

The central claim rests on empirical benchmarking rather than new theoretical axioms or postulated entities; any free parameters are likely algorithm hyperparameters tuned to the benchmark but are not enumerated in the abstract.

free parameters (1)
  • QAIAs hyperparameters
    Tuning parameters for the quantum-annealing-inspired sampling procedure that affect solution quality and speed; values not specified in abstract.

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