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arxiv: 2501.19221 · v2 · submitted 2025-01-31 · 🪐 quant-ph · physics.comp-ph

VeloxQ: A Fast and Efficient QUBO Solver

J. Paw{\l}owski , J. Tuziemski , P. Tarasiuk , H. Louzada , R. Adamski , K. Hendzel , {\L}. Pawela , B. Gardas This is my paper

Pith reviewed 2026-05-23 04:36 UTC · model grok-4.3

classification 🪐 quant-ph physics.comp-ph
keywords QUBO solverQuadratic Unconstrained Binary Optimizationclassical optimizationquantum annealingscalabilitybenchmarkingsparse instancesbinary optimization
0
0 comments X

The pith

VeloxQ solves large QUBO problems on ordinary computers and scales to instances with 10^8 variables where others cannot.

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

The paper presents VeloxQ as a solver for Quadratic Unconstrained Binary Optimization problems that runs on standard computing hardware. Through extensive benchmarks against quantum annealers, physics-inspired methods, and classical solvers like CPLEX, it shows competitive or superior solution quality and runtimes across native topologies, embedded problems, HUBO-derived cases, and planted-solution tests. VeloxQ stands out for its ability to process the largest sparse instances up to 10^8 variables within practical time limits, unlike the other methods tested. This offers an immediate option for optimization tasks in areas such as scheduling and machine learning without requiring specialized quantum devices.

Core claim

VeloxQ delivers competitive solution quality and runtime across the benchmark suite of native quantum-annealer topologies, embedded all-to-all instances, HUBO-derived instances, planted-solution instances, certified-solver regimes, and dense Branch-and-Bound test cases; in several regimes it outperforms the compared solvers and is the only method runnable on the largest sparse instances with up to 10^8 sparsely connected variables within the computational budget.

What carries the argument

VeloxQ, a solver for Quadratic Unconstrained Binary Optimization (QUBO) problems implemented on conventional computing infrastructure.

Load-bearing premise

The benchmark instances and comparison protocols are representative of practical QUBO difficulty with runtime and quality metrics measured under equivalent conditions across platforms.

What would settle it

A new set of large sparse QUBO instances with 10^8 variables on which VeloxQ produces lower-quality solutions or requires more runtime than at least one compared solver such as D-Wave or CPLEX.

Figures

Figures reproduced from arXiv: 2501.19221 by B. Gardas, H. Louzada, J. Paw{\l}owski, J. Tuziemski, K. Hendzel, {\L}. Pawela, P. Tarasiuk, R. Adamski.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
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Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
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Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
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Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
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Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
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Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
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Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
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Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
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Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
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Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Since these instances are also randomized, for each size we have prepared 10 copies and averaged the results, again omitting the error bars for clarity. With a little optimization, VeloxQ can consistently find the ground state for even the largest instances with 90k vari￾ables, in the easy regime. Nevertheless, the default set￾tings are already sufficient to outperform PA and SBM in both difficulty regime… view at source ↗
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Figure 13. Figure 13: FIG. 13 [PITH_FULL_IMAGE:figures/full_fig_p013_13.png] view at source ↗
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Figure 14. Figure 14: FIG. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_14.png] view at source ↗
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Figure 15. Figure 15: FIG. 15 [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
read the original abstract

We introduce VeloxQ, a fast solver for Quadratic Unconstrained Binary Optimization (QUBO) problems, which are central to many real-world optimization tasks. Unlike approaches that depend on emerging quantum hardware, VeloxQ can be deployed on conventional computing infrastructure. We benchmark VeloxQ against state-of-the-art QUBO solvers from several families. These include quantum annealers, specifically D-Wave's Advantage and Advantage2 platforms; the digital-quantum BF-DCQO algorithm for Higher-Order Unconstrained Binary Optimization (HUBO) developed by Kipu Quantum; physics-inspired algorithms including Simulated Bifurcation, Parallel Annealing, and tropical tensor networks; and conventional methods including CPLEX, brute force, BEIT's Chimera solver, and Branch-and-Bound variants. The benchmark suite covers native quantum-annealer topologies, embedded all-to-all instances, HUBO-derived instances, planted-solution instances, certified-solver regimes, and dense Branch-and-Bound test cases. Across the benchmark suite, VeloxQ delivers competitive solution quality and runtime, and in several regimes outperforms the compared solvers. VeloxQ also demonstrates strong scalability. Among the solvers considered in this study, it was the only method we could run on the largest sparse instances within our computational budget, including problems with up to $10^{8}$ sparsely connected variables. These findings position VeloxQ as a competitive and practical tool for tackling large-scale QUBO/HUBO problems, offering a practical alternative to existing quantum and classical optimization methods.

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

0 major / 3 minor

Summary. The manuscript introduces VeloxQ, a classical solver for Quadratic Unconstrained Binary Optimization (QUBO) problems deployable on conventional hardware. It benchmarks VeloxQ against quantum annealers (D-Wave Advantage and Advantage2), the BF-DCQO algorithm, physics-inspired methods (Simulated Bifurcation, Parallel Annealing, tropical tensor networks), and classical solvers (CPLEX, brute force, BEIT Chimera, Branch-and-Bound). The benchmark suite includes native topologies, embedded all-to-all instances, HUBO-derived problems, planted-solution instances, certified regimes, and dense test cases. The central empirical claim is that VeloxQ achieves competitive solution quality and runtime, outperforms comparators in several regimes, and is the only solver runnable on the largest sparse instances (up to 10^8 variables) within the computational budget.

Significance. If the benchmark protocols and results are reproducible and the implementation details are fully specified, the work would be significant as a practical classical baseline for large-scale QUBO/HUBO problems. The explicit comparison across quantum and classical families on a diverse suite, together with the reported scalability to 10^8-variable sparse instances, provides a concrete data point on the current reach of classical methods versus quantum-inspired approaches.

minor comments (3)
  1. [Abstract] Abstract: the statement that VeloxQ 'outperforms the compared solvers' in several regimes would be strengthened by at least one quantitative example (e.g., a specific runtime or quality ratio on a named instance family) rather than remaining purely qualitative.
  2. The manuscript should include a dedicated section or appendix describing the algorithmic core of VeloxQ (pseudocode, key heuristics, or complexity statements) so that the performance claims can be assessed independently of the benchmark tables.
  3. Benchmark description: clarify whether all solvers were run with default parameters or with instance-specific tuning, and whether wall-clock time includes embedding or preprocessing steps for the quantum platforms.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of VeloxQ and the recommendation for minor revision. The report correctly identifies the paper's focus on providing a practical classical baseline with extensive cross-family benchmarks and scalability to 10^8-variable instances. No major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity; empirical benchmark paper

full rationale

The paper introduces VeloxQ and presents empirical benchmark comparisons against quantum annealers, physics-inspired algorithms, and classical solvers across native topologies, embedded instances, HUBO-derived cases, planted solutions, and large sparse problems up to 10^8 variables. No derivation chain, equations, fitted parameters, or self-citation load-bearing steps are described. The central claims are performance statements grounded in reported runtime and quality metrics rather than any mathematical reduction to inputs. This is a standard empirical report with no internal circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no information on free parameters, axioms, or invented entities inside the solver; the ledger is therefore empty by default.

pith-pipeline@v0.9.0 · 5842 in / 1129 out tokens · 39946 ms · 2026-05-23T04:36:40.626226+00:00 · methodology

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Forward citations

Cited by 3 Pith papers

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

  1. Simulated Bifurcation Quantum Annealing

    quant-ph 2026-04 unverdicted novelty 6.0

    SBQA adds inter-replica interactions to simulated bifurcation to mimic quantum tunneling and improves performance on sparse rugged optimization problems over standard SBM.

  2. Quantum-inspired dynamical models on quantum and classical annealers

    quant-ph 2025-09 unverdicted novelty 6.0

    A parallel-in-time encoding turns quantum dynamical propagators into QUBO instances for direct benchmarking of quantum annealers against classical solvers on models from single-qubit rotations to PT-symmetric systems.

  3. Recent quantum runtime (dis)advantages

    quant-ph 2025-10 conditional novelty 5.0

    End-to-end runtime definitions and strong classical baselines show that three recent quantum advantage claims in annealing, Simon's problem, and hybrid algorithms do not hold on NISQ hardware.

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