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arxiv: 2604.25162 · v2 · submitted 2026-04-28 · 🪐 quant-ph

Recognition: unknown

Experimental Workflows for Combinatorial Optimization: Towards Quantum Advantage

Prashanti Priya Angara , Luis F. Rivera , Ulrike Stege , Hausi M\"uller , Ibrahim Shehzad , Sean Wagner
Authors on Pith no claims yet

Pith reviewed 2026-05-07 16:54 UTC · model grok-4.3

classification 🪐 quant-ph
keywords hybrid quantum-classical workflowsQAOAgraph optimizationcombinatorial optimizationquantum hardware experimentsminimum vertex covermaximum independent setmaximum clique
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The pith

A hybrid workflow reduces graph problems for QAOA then maps results back classically to solve instances up to 128 vertices on current hardware.

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

The paper develops a sandbox platform that tests complete pipelines for graph optimization: classical pre-processing shrinks the instance, QAOA solves the resulting unconstrained version on quantum hardware, and classical post-processing recovers high-quality feasible solutions. This is applied to minimum vertex cover, maximum independent set, and maximum clique on synthetic graphs, benchmarks, and real networks, with hardware runs reaching 128 vertices and 128 qubits. The end-to-end experiments clarify how to partition work between classical and quantum steps and how to judge whether quantum outputs are useful. A reader would care because the method gives a practical way to run and interpret quantum optimization on today's devices without waiting for larger, error-corrected machines.

Core claim

By reducing constrained graph problems to smaller unconstrained forms via classical pre-processing, applying QAOA to those forms on IBM quantum processors, and recovering feasible solutions through classical post-processing, the workflow produces usable results for vertex cover, independent set, and clique on graphs up to 128 vertices, with circuits using up to 128 qubits and over 13,000 two-qubit gates, as shown in hardware experiments.

What carries the argument

The hybrid workflow that uses classical pre-processing to reduce instance size, runs QAOA on the reduced unconstrained problem, and applies classical post-processing to map outputs to feasible solutions.

If this is right

  • The workflow avoids the need to encode constraints directly into the quantum circuit.
  • End-to-end testing on real hardware up to 128 vertices exposes practical bottlenecks in workload partitioning.
  • The platform supplies a repeatable method for domain experts to interpret quantum outputs and gauge utility.
  • Results from synthetic, benchmark, and real-world networks illustrate how such pipelines behave across problem scales.

Where Pith is reading between the lines

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

  • If the reduction step preserves solution quality well, the same structure could be reused as qubit counts increase.
  • The sandbox could be extended to test other quantum algorithms or problem classes that reduce to graphs.
  • Systematic comparison of these hybrid outputs against classical heuristics on the same instances would give clearer evidence of any advantage.
  • Practitioners in logistics or network design might adapt the pre- and post-processing templates to their own constrained problems.

Load-bearing premise

The classical reduction and mapping steps produce solutions whose quality can be compared fairly to classical solvers without introducing systematic bias.

What would settle it

Running the workflow on a collection of known hard graph instances and finding that its final solution quality is consistently and substantially worse than standard classical solvers such as branch-and-bound or local search, beyond what approximation ratios explain.

Figures

Figures reproduced from arXiv: 2604.25162 by Hausi M\"uller, Ibrahim Shehzad, Luis F. Rivera, Prashanti Priya Angara, Sean Wagner, Ulrike Stege.

Figure 1
Figure 1. Figure 1: End-to-end classical-quantum pipeline for solving combinatorial optimization problems via the profit framework. The view at source ↗
Figure 2
Figure 2. Figure 2: QAOA solver performance on synthetic graph instances. view at source ↗
read the original abstract

Demonstrating quantum advantage for combinatorial optimization requires more than standalone algorithmic results; it calls for end-to-end case studies that integrate problem modelling, quantum execution, and classical refinement into practical workflows. This paper presents a sandbox platform for experimenting with hybrid quantum-classical workflows in graph optimization, enabling the systematic study of end-to-end optimization pipelines. Using our platform, we investigate three classically intractable and mutually reducible graph problems -- Minimum Vertex Cover, Maximum Independent Set, and Maximum Clique -- by transforming them into an unconstrained problem and solving the resulting instances with QAOA on IBM platforms. Our workflow combines classical pre-processing to reduce instance size, quantum optimization on the reduced problem, and classical postprocessing to map quantum outputs to high-quality feasible solutions, thereby avoiding direct constraint encoding in the quantum circuit. We evaluate the approach on synthetic graphs, benchmark instances, and real-world networks, and report hardware experiments on IBM Quantum System One at PINQ2 in Bromont, Quebec, powered by IBM's 156-qubit Heron r2 processor on graphs up to 128 vertices, with circuits involving up to 128 qubits and 13,555 two-qubit gates. The results illustrate how sandbox-style end-to-end experimentation can expose bottlenecks, clarify the role of classical-quantum workload partitioning, and provide domain experts and practitioners with a practical guide for interpreting quantum optimization outputs and assessing quantum utility on the road to quantum advantage in combinatorial optimization.

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 / 2 minor

Summary. The manuscript presents a sandbox platform for hybrid quantum-classical workflows targeting three mutually reducible graph problems (Minimum Vertex Cover, Maximum Independent Set, and Maximum Clique). The approach uses classical pre-processing to shrink instances, QAOA to optimize the resulting unconstrained problems on IBM Quantum hardware (Heron r2 processor), and classical post-processing to recover feasible high-quality solutions, with experiments reported on synthetic, benchmark, and real-world graphs up to 128 vertices using circuits of up to 128 qubits and 13,555 two-qubit gates.

Significance. If the experiments include quantitative evidence that the QAOA outputs on reduced instances supply starting points yielding meaningfully better feasible solutions than classical methods alone on the same reduced graphs, the work would supply a concrete end-to-end case study and practical guidance for partitioning workloads in quantum optimization. The platform's focus on exposing bottlenecks and interpreting outputs is a constructive contribution to the literature on hybrid algorithms.

major comments (2)
  1. [Abstract and Results] The abstract and experimental sections report hardware scale (128 vertices, 13,555 two-qubit gates) but contain no quantitative metrics such as approximation ratios, optimality gaps versus Gurobi/CPLEX on identical reduced instances, or ablation results removing the QAOA layer. This omission leaves the central claim that the workflow demonstrates a viable path to quantum utility unsupported, as the skeptic correctly notes that classical pre- and post-processing could dominate solution quality.
  2. [Workflow Description and Experiments] No data or analysis is provided to test whether the classical reduction and post-processing steps introduce biases that invalidate comparisons of solution quality; without such checks (e.g., performance of classical heuristics on the reduced graphs before and after QAOA), the claim that the quantum step supplies high-quality feasible solutions cannot be evaluated.
minor comments (2)
  1. [Introduction and Methods] The description of the three graph problems and their reductions would benefit from explicit equations or pseudocode in the methods section to clarify how constraints are avoided in the quantum circuit.
  2. [Figures and Tables] Figure captions and table headers should explicitly state the number of instances, graph types, and exact metrics plotted to improve readability of the experimental results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments correctly identify that the current manuscript prioritizes description of the sandbox platform and hardware-scale demonstrations over direct quantitative benchmarking of the quantum step against classical baselines on the reduced instances. We agree this limits the strength of claims about the quantum component's contribution and will revise the manuscript to address both points with additional analysis and metrics drawn from the existing experimental data.

read point-by-point responses

  1. Referee: [Abstract and Results] The abstract and experimental sections report hardware scale (128 vertices, 13,555 two-qubit gates) but contain no quantitative metrics such as approximation ratios, optimality gaps versus Gurobi/CPLEX on identical reduced instances, or ablation results removing the QAOA layer. This omission leaves the central claim that the workflow demonstrates a viable path to quantum utility unsupported, as the skeptic correctly notes that classical pre- and post-processing could dominate solution quality.

    Authors: We agree that the absence of these metrics weakens the ability to isolate the QAOA contribution. The manuscript frames the work as a platform for end-to-end experimentation rather than a claim of quantum advantage, but the referee is correct that readers will expect evidence that the quantum layer adds value beyond the classical reduction and post-processing. In revision we will add (i) approximation ratios for the QAOA outputs on the reduced instances, (ii) optimality gaps relative to Gurobi/CPLEX run on the same reduced graphs, and (iii) an ablation comparing the full workflow against classical heuristics applied directly to the reduced instances. These additions will be placed in the experimental results section and referenced in the abstract. revision: yes

  2. Referee: [Workflow Description and Experiments] No data or analysis is provided to test whether the classical reduction and post-processing steps introduce biases that invalidate comparisons of solution quality; without such checks (e.g., performance of classical heuristics on the reduced graphs before and after QAOA), the claim that the quantum step supplies high-quality feasible solutions cannot be evaluated.

    Authors: The referee correctly notes that without explicit checks, it is impossible to rule out that any observed solution quality stems entirely from the classical pre- and post-processing. We will add a new subsection that reports the performance of standard classical heuristics (e.g., greedy and local search) on the reduced graphs both before and after the QAOA layer. This will include direct comparison of solution quality and feasibility rates, allowing readers to assess whether the quantum optimization step provides measurable improvement or introduces any systematic bias. The analysis will be performed on the same set of synthetic, benchmark, and real-world instances already presented. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental workflow paper reports direct hardware results without self-referential derivations

full rationale

The paper describes an experimental sandbox platform for hybrid quantum-classical graph optimization workflows, including classical pre-processing to reduce instance size, QAOA execution on reduced unconstrained problems, and classical post-processing to recover feasible solutions. No mathematical derivation chain, first-principles predictions, or fitted parameters are presented that reduce to their own inputs by construction. Claims rest on reported hardware experiments (up to 128 vertices, 13,555 two-qubit gates on IBM Heron) and empirical observations about bottlenecks and workload partitioning, which are externally verifiable through the described runs rather than logical self-equivalence. The absence of any ansatz smuggling, uniqueness theorems, or renamed empirical patterns as novel results keeps the presentation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No mathematical derivations, free parameters, or new postulated entities are introduced in the abstract; the work relies on standard assumptions of QAOA applicability and classical reduction techniques from prior literature.

pith-pipeline@v0.9.0 · 5571 in / 1130 out tokens · 29032 ms · 2026-05-07T16:54:20.392701+00:00 · methodology

discussion (0)

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