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Quantum Stochastic Gradient Descent in its continuous-time limit based on the Wigner formulation of Open Quantum Systems

Jose A. Morales Escalante
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⚡ Quantum Brief
A new theoretical framework bridges classical and quantum optimization by adapting stochastic gradient descent (SGD) into a continuous-time quantum algorithm using the Wigner formulation of open quantum systems. Researcher José A. Morales Escalante proposes leveraging the Wigner function—a phase-space representation—to translate probabilistic classical algorithms into quantum equivalents, enabling hybrid optimization techniques. The work focuses on SGD’s quantum analog, where noise and dissipation in open quantum systems replace classical stochasticity, potentially accelerating convergence in machine learning and optimization tasks. Published in October 2025, the preprint spans quantum physics, mathematical optimization, and computational physics, targeting interdisciplinary applications in quantum-enhanced algorithms. This approach could unify classical and quantum probabilistic methods, offering a pathway to scalable quantum machine learning by exploiting continuous-time dynamics in open quantum systems.
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Quantum Physics arXiv:2510.25910 (quant-ph) [Submitted on 29 Oct 2025] Title:Quantum Stochastic Gradient Descent in its continuous-time limit based on the Wigner formulation of Open Quantum Systems Authors:Jose A.

Morales Escalante View a PDF of the paper titled Quantum Stochastic Gradient Descent in its continuous-time limit based on the Wigner formulation of Open Quantum Systems, by Jose A.

Morales Escalante View PDF Abstract:The main ideas behind a research plan to use the Wigner formulation as a bridge between classical and quantum probabilistic algorithms are presented, focusing on a particular case: the Quantum analog of Stochastic Gradient Descent in its continuous-time limit based on the Wigner formulation of Open Quantum Systems. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Numerical Analysis (math.NA); Optimization and Control (math.OC); Computational Physics (physics.comp-ph) Cite as: arXiv:2510.25910 [quant-ph] (or arXiv:2510.25910v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.25910 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jose Morales Escalante [view email] [v1] Wed, 29 Oct 2025 19:24:57 UTC (422 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Stochastic Gradient Descent in its continuous-time limit based on the Wigner formulation of Open Quantum Systems, by Jose A. Morales EscalanteView PDF view license Current browse context: quant-ph new | recent | 2025-10 Change to browse by: cs cs.NA math math-ph math.MP math.NA math.OC physics physics.comp-ph 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?)

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