Degeneracy Counting Quantum Algorithm using Decoherence

[2608.14941] Degeneracy Counting Quantum Algorithm using Decoherence Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2608.14941 (cs) [Submitted on 14 Aug 2026] Title: Degeneracy Counting Quantum Algorithm using Decoherence Authors: Malay Marut Das , Mark A. Novotny , Yaroslav Koshka View a PDF of the paper titled Degeneracy Counting Quantum Algorithm using Decoherence, by Malay Marut Das and 2 other authors View PDF Abstract: Counting the global optima of a classical optimization problem is a #P-hard task. We develop the canonical thermal pure quantum (CTPQ) state-based degeneracy counting (CTPQsd#) algorithm that determines the number of global optima of a classical optimization problem P by measuring only a small probe S, without finding individual minima. The method exploits a perturbative relation between the decoherence measure of S and the degeneracy of P when S and P are together in a CTPQ state. We provide the first numerical demonstration that this relation can be used to count the global minima, applying it to problems encoded by diagonal random-energy Hamiltonians as a maximally unstructured testbed for classical binary optimization problems. Classical simulations of up to 20 problem qubits quantify the algorithm's sensitivity to variations in the temperature of the CTPQ state, the Hamiltonian energy range, the problem size, and degeneracy. We establish the temperature threshold for determining the exact degeneracy and identify a second, lower threshold that provides a temperature window to count near-degenerate minima within a user-defined energy tolerance. By confining measurement to S, the protocol replaces tomography over the exponentially large problem Hilbert space with tomography over a small probe represented by only four qubits. Subjects: Machine Learning (cs.LG) ; Quantum Physics (quant-ph) Cite as: arXiv:2608.14941 [cs.LG] (or arXiv:2608.14941v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2608.14941 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Malay Das [ view email ] [v1] Fri, 14 Aug 2026 23:41:15 UTC (1,082 KB) Full-text links: Access Paper: View a PDF of the paper titled Degeneracy Counting Quantum Algorithm using Decoherence, by Malay Marut Das and 2 other authors View PDF view license Current browse context: cs.LG < prev | next > new | recent | 2026-08 Change to browse by: cs quant-ph References & Citations INSPIRE HEP NASA ADS Google 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? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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