Locally Acting Grover Mixers for Constraint-Preserving QAOA

Quantum Physics arXiv:2606.11530 (quant-ph) [Submitted on 10 Jun 2026] Title:Locally Acting Grover Mixers for Constraint-Preserving QAOA Authors:Minjin Choi, Dongkeun Lee, Junghee Ryu View a PDF of the paper titled Locally Acting Grover Mixers for Constraint-Preserving QAOA, by Minjin Choi and Dongkeun Lee and Junghee Ryu View PDF HTML (experimental) Abstract:The Grover mixer quantum alternating operator ansatz (GM-QAOA) employs the Grover mixer to confine the quantum evolution to the feasible subspace defined by the problem. Its mixing unitary, however, requires a global multi-controlled phase-shift gate acting on all qubits, resulting in substantial circuit overhead on near-term quantum devices. In this work, we propose locally acting Grover mixers tailored to initial states that admit a product structure over disjoint qubit subsystems, which may be obtained by encoding only a subset of problem constraints into the initial state preparation. The proposed method preserves the search space defined by the initial state while significantly lowering implementation cost, as the global multi-controlled phase-shift gate is replaced with local operations on disjoint subsystems. Numerical simulations on the exact-cover problem and the traveling salesman problem (TSP) demonstrate that the proposed method achieves convergence behavior comparable to that of the original GM-QAOA, while using shallower circuits with fewer gates. We further compare two constraint encoding strategies for the TSP, encoding only a subset of constraints versus all constraints into the initial state preparation, and show that the former combined with the proposed mixer yields markedly more compact circuits at the point where comparable solution quality is achieved. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.11530 [quant-ph] (or arXiv:2606.11530v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.11530 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Minjin Choi [view email] [v1] Wed, 10 Jun 2026 00:27:49 UTC (418 KB) Full-text links: Access Paper: View a PDF of the paper titled Locally Acting Grover Mixers for Constraint-Preserving QAOA, by Minjin Choi and Dongkeun Lee and Junghee RyuView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?) 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?)