Constrained Quantum Optimization at Utility Scale: Application to the Knapsack Problem
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Quantum Physics arXiv:2603.00260 (quant-ph) [Submitted on 27 Feb 2026] Title:Constrained Quantum Optimization at Utility Scale: Application to the Knapsack Problem Authors:Naeimeh Mohseni, Julien-Pierre Houle, Ibrahim Shehzad, Giorgio Cortiana, Corey O'Meara, Adam Bene Watts View a PDF of the paper titled Constrained Quantum Optimization at Utility Scale: Application to the Knapsack Problem, by Naeimeh Mohseni and 5 other authors View PDF HTML (experimental) Abstract:Constrained combinatorial optimization problems are challenging for quantum computing, particularly at utility-relevant scales and on near-term hardware. At the same time, these problems are of practical significance in industry; for example, the Unit Commitment (UC) problem in energy systems involves complex operational constraints. To address this challenge, we apply copula-QAOA (cop-QAOA), a hardware-efficient approach for constrained optimization to a single-period UC that can be reduced to a one-dimensional knapsack. Cop-QAOA biases the quantum state toward feasible solutions using constant-depth mixers and appropriately biased initial states. We implement our benchmark on problem instances that are confirmed to be hard for classical solvers such as Gurobi. Our results show that cop-QAOA often finds solutions better than a lazy greedy baseline and very close to, and in some instances surpasses, those obtained by Gurobi, with only a few QAOA rounds. This work presents the largest successful demonstration of the knapsack problem on IBM Quantum hardware using up to 150 qubits, and more generally, the largest demonstration of constrained combinatorial optimization where constraints are enforced via shallow mixers. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.00260 [quant-ph] (or arXiv:2603.00260v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.00260 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Naeimeh Mohseni [view email] [v1] Fri, 27 Feb 2026 19:16:28 UTC (1,783 KB) Full-text links: Access Paper: View a PDF of the paper titled Constrained Quantum Optimization at Utility Scale: Application to the Knapsack Problem, by Naeimeh Mohseni and 5 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)