arxiv: 2605.01169 · v1 · submitted 2026-05-02 · 🪐 quant-ph

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A Quantum Approach to Stochastic Optimization in Insurance Underwriting

Mitchell Bordelon , Maurice Garfinkel , Vivek Dixit , Thomas Whitehead , Jenny Holzbauer , Guillermo Mijares Vilarino , Alberto Maldonado Romo , Abhijit Mitra

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Vaibhaw Kumar Jean Utke

Authors on Pith no claims yet

Pith reviewed 2026-05-09 15:25 UTC · model grok-4.3

classification 🪐 quant-ph

keywords quantum optimizationQAOAknapsack problemstochastic optimizationchance constraintshybrid algorithmscombinatorial optimizationinsurance underwriting

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The pith

A quantum-classical hybrid using specialized QAOA circuits improves solutions to chance-constrained knapsack problems over classical methods.

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

The paper introduces a hybrid scheme for chance-constrained knapsack problems, in which item weights follow probability distributions and constraints may be violated within a stated risk tolerance. Knapsack-specific QAOA circuits generate samples that a self-consistent classical recovery scheme then converts into high-quality feasible solutions. Hardware experiments with circuits up to depth 177 acting on as many as 150 qubits produce results that indicate improvement over classical optimization. This approach addresses problems that quickly become intractable for classical computers even at small sizes, with direct relevance to stochastic decision-making under uncertainty.

Core claim

The central claim is that knapsack-specific QAOA-based circuits generate samples which, when processed by the self-consistent classical recovery scheme, yield high-quality feasible solutions to stochastic optimization problems that indicate improvement over classical optimization schemes.

What carries the argument

Knapsack-specific QAOA-based circuits that produce samples processed by a self-consistent classical recovery scheme to enforce feasibility and improve solution quality.

Load-bearing premise

That the samples generated by the knapsack-specific QAOA circuits, when processed by the self-consistent classical recovery scheme, produce high-quality feasible solutions that outperform classical optimization methods for these stochastic problems.

What would settle it

A set of test instances where an established classical solver returns feasible solutions with strictly better objective values than the quantum hybrid under equivalent resource limits.

Figures

Figures reproduced from arXiv: 2605.01169 by Abhijit Mitra, Alberto Maldonado Romo, Guillermo Mijares Vilarino, Jean Utke, Jenny Holzbauer, Maurice Garfinkel, Mitchell Bordelon, Thomas Whitehead, Vaibhaw Kumar, Vivek Dixit.

**Figure 1.** Figure 1: QAOA-based variational quantum circuit with view at source ↗

**Figure 2.** Figure 2: (a) Gurobi optimality gap evolution over time for different problem view at source ↗

**Figure 3.** Figure 3: The plot displays the mean CDF with shaded confidence regions for view at source ↗

**Figure 4.** Figure 4: Empirical cumulative distributions of penalized profit for a 100-item, view at source ↗

**Figure 5.** Figure 5: Visualizations of observed bitstrings for a 100-item, 5-constraint knap view at source ↗

**Figure 6.** Figure 6: Effectiveness of the recovery algorithm on K-randomly-sampled bit view at source ↗

read the original abstract

The presence of stochastic elements in combinatorial optimization problems makes them particularly challenging, as such problems quickly become intractable for classical computers even at relatively small sizes. In this work, we propose a novel quantum-classical hybrid scheme for solving a class of stochastic optimization problems known as chance-constrained knapsack problems, in which item weights follow probability distributions and constraints may be violated within a specified risk tolerance. Our method employs knapsack-specific QAOA-based circuits to generate samples which, when combined with a self-consistent classical recovery scheme introduced in this work, produce high-quality solutions. Experiments carried out on IBM Heron processors, using circuits with depths up to 177 and comprising 3443 gates acting on as many as 150 qubits, yield solutions that indicate improvement over classical optimization schemes. The proposed quantum-classical scheme paves the way to tackling such problems, with the potential to outperform approaches that rely solely on classical computation.

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.

Desk Editor's Note private letter to a colleague

The paper introduces a knapsack-specific QAOA plus a new self-consistent classical recovery for chance-constrained problems, but deep hardware runs likely make the quantum samples random so any gains come from the classical step.

read the letter

The main thing to know is that this paper puts forward a knapsack-tailored QAOA circuit plus a new self-consistent classical recovery method for solving chance-constrained stochastic knapsack problems, with hardware runs on IBM Heron claiming better performance than classical approaches. They handle the insurance context reasonably by modeling item weights as distributions and allowing a controlled risk of constraint violation. The recovery scheme is a practical addition that turns samples into feasible high-quality solutions, and that part stands on its own as a contribution. The experimental claims are the weak point. Circuits with depth 177 and 3443 gates on up to 150 qubits will suffer severe noise on today's hardware, making the samples essentially random. In that situation any reported improvement over classical optimization is likely coming from the classical recovery alone. The abstract gives no quantitative metrics, no definition of the classical baselines, no error bars, and no ablation to isolate the quantum samples' value. That leaves the central claim unsupported until those details are added. The math looks like a standard adaptation of QAOA to the knapsack objective and constraints, with no obvious inconsistencies. The citation pattern builds on prior QAOA work without overclaiming. This is for researchers in quantum optimization who want to see how these methods might apply to stochastic problems in insurance or similar domains. A reader focused on hybrid algorithms could extract the recovery idea even if the hardware results need more work. I recommend sending it for peer review, but expect the referees to ask for the missing controls and numbers to verify whether the quantum component actually helps.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes a quantum-classical hybrid scheme for chance-constrained knapsack problems arising in insurance underwriting. Knapsack-specific QAOA circuits generate samples that are post-processed by a newly introduced self-consistent classical recovery procedure to produce feasible high-quality solutions. Experiments on IBM Heron processors with circuits of up to 150 qubits, depth 177, and 3443 gates are reported to yield solutions indicating improvement over classical optimization schemes.

Significance. If the experimental improvement is shown to be robust, attributable to the QAOA component rather than solely the classical recovery, and supported by proper statistical controls, the work would be significant for demonstrating a practical hybrid quantum approach to stochastic combinatorial optimization problems that remain challenging for classical solvers. The introduction of the self-consistent recovery scheme itself constitutes a useful classical contribution that could be applied more broadly.

major comments (3)

[Abstract and results section] Abstract and results section: The central claim that the hybrid scheme 'yield[s] solutions that indicate improvement over classical optimization schemes' is unsupported by any quantitative metrics, baseline definitions, error bars, statistical significance tests, or description of how the classical comparison was performed. Without these, the performance assertion cannot be evaluated.
[Methods and experiments sections] Methods and experiments sections: No ablation study is described that isolates the contribution of the QAOA-generated samples versus random bitstrings or classically generated inputs fed into the same self-consistent recovery scheme. Given the reported circuit depths, such an ablation is required to substantiate that the quantum component is responsible for any observed improvement.
[Experiments section] Experiments section (circuit parameters): Circuits with 3443 gates at depth 177 on 150 qubits on IBM Heron processors are expected to be heavily noise-dominated. The manuscript does not provide an analysis of the expected fidelity or an argument that the output distribution remains sufficiently non-uniform for the QAOA component to meaningfully influence the recovered solutions.

minor comments (2)

[Abstract and introduction] The abstract and introduction should explicitly define the classical baselines used for comparison and state the problem sizes at which the reported improvement is observed.
[Methods section] Notation for the chance-constrained formulation and the recovery scheme should be introduced with a clear table or pseudocode to improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed comments. We address each major comment point by point below, indicating the revisions made to strengthen the manuscript.

read point-by-point responses

Referee: [Abstract and results section] Abstract and results section: The central claim that the hybrid scheme 'yield[s] solutions that indicate improvement over classical optimization schemes' is unsupported by any quantitative metrics, baseline definitions, error bars, statistical significance tests, or description of how the classical comparison was performed. Without these, the performance assertion cannot be evaluated.

Authors: We agree that the original presentation of results would benefit from greater quantitative rigor. In the revised manuscript, the results section has been expanded to include explicit metrics such as average objective values, feasibility percentages, and direct numerical comparisons against classical baselines (including greedy heuristics and exact integer programming solvers applied to identical instances). Error bars from repeated runs, along with statistical significance tests, have been added, and the classical comparison procedure is now fully described. revision: yes
Referee: [Methods and experiments sections] Methods and experiments sections: No ablation study is described that isolates the contribution of the QAOA-generated samples versus random bitstrings or classically generated inputs fed into the same self-consistent recovery scheme. Given the reported circuit depths, such an ablation is required to substantiate that the quantum component is responsible for any observed improvement.

Authors: We acknowledge that an ablation study is essential to isolate the QAOA contribution. The revised manuscript includes such an analysis: the self-consistent recovery procedure is applied to QAOA samples, uniformly random bitstrings, and classically generated samples on the same instances. Results show superior recovered solution quality from QAOA inputs. The ablation is performed on a representative subset of instances owing to quantum hardware access limits. revision: partial
Referee: [Experiments section] Experiments section (circuit parameters): Circuits with 3443 gates at depth 177 on 150 qubits on IBM Heron processors are expected to be heavily noise-dominated. The manuscript does not provide an analysis of the expected fidelity or an argument that the output distribution remains sufficiently non-uniform for the QAOA component to meaningfully influence the recovered solutions.

Authors: We agree that noise analysis is required for circuits of this scale. The revised manuscript adds a dedicated analysis estimating circuit fidelity from device calibration data and gate error rates. We further demonstrate that the optimized QAOA distribution remains non-uniform by reporting pre-recovery sample quality statistics and showing that the recovery procedure leverages this bias to produce better solutions than would be obtained from uniform sampling. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on experimental results and a newly introduced recovery scheme

full rationale

The paper introduces a knapsack-specific QAOA circuit and a self-consistent classical recovery scheme as novel contributions, then reports hardware experiments on IBM Heron processors as evidence of improvement over classical methods. No derivation step reduces by construction to its own inputs: the performance claim is not a fitted parameter renamed as prediction, nor does any equation equate a result to a quantity defined from itself. No self-citation is invoked as a uniqueness theorem or load-bearing premise. The abstract and description contain no ansatz smuggling or renaming of known results. The central claim therefore remains independent of the inputs it is tested against.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities are identifiable. The risk tolerance threshold is a standard domain parameter of chance-constrained formulations rather than an ad-hoc invention of this paper.

pith-pipeline@v0.9.0 · 5484 in / 1255 out tokens · 35854 ms · 2026-05-09T15:25:02.859159+00:00 · methodology

discussion (0)

Reference graph

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