Iterative warm-start optimization with quantum imaginary time evolution
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Quantum Physics arXiv:2604.26047 (quant-ph) [Submitted on 28 Apr 2026] Title:Iterative warm-start optimization with quantum imaginary time evolution Authors:Phillip C. Lotshaw, Titus Morris, Stuart Hadfield, Ryan Bennink View a PDF of the paper titled Iterative warm-start optimization with quantum imaginary time evolution, by Phillip C. Lotshaw and Titus Morris and Stuart Hadfield and Ryan Bennink View PDF HTML (experimental) Abstract:Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand, then samples the states to determine an approximately optimal solution. However, promising alternative approaches have considered ``warm-start" and sampling-based methods that instead begin from the best known solution, which can be directly optimized with the quantum computer and updated as new information becomes available, potentially outperforming the fixed ansätze. Here we use these ideas to design a nonvariational quantum algorithm for combinatorial optimization. At each step the algorithm begins with a state superposed around the best known solution, then drives it to lower energy using quantum imaginary time evolution. These nonvariational, initial-state-dependent circuits are determined using analytic equations that are evaluated using only a conventional computer. After implementing the circuits, the state is sampled, potentially obtaining a new best-known solution to use as the initial state at the next iteration. Using simulations of the algorithm solving MaxCut on 3-regular graphs with 30 or fewer vertices and a shot budget of 100 total shots, the approach obtains median solutions within 95\% of the global optimum and finds optimal solutions in 11\% or more of cases, significantly outperforming random and simplified classical search procedures. We discuss several future directions. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.26047 [quant-ph] (or arXiv:2604.26047v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.26047 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Phillip Lotshaw [view email] [v1] Tue, 28 Apr 2026 18:32:11 UTC (103 KB) Full-text links: Access Paper: View a PDF of the paper titled Iterative warm-start optimization with quantum imaginary time evolution, by Phillip C. Lotshaw and Titus Morris and Stuart Hadfield and Ryan BenninkView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)