Quantum-to-Classical Computability Transition via Negative Markov Chains
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Quantum Physics arXiv:2604.19889 (quant-ph) [Submitted on 21 Apr 2026] Title:Quantum-to-Classical Computability Transition via Negative Markov Chains Authors:Hugo Lóio, Jacopo De Nardis, Tony Jin View a PDF of the paper titled Quantum-to-Classical Computability Transition via Negative Markov Chains, by Hugo L\'oio and 1 other authors View PDF HTML (experimental) Abstract:We develop a recently introduced representation of quantum dynamics based on sampling negative Markov chain processes. By introducing particles and antiparticles, this formalism maps generic quantum dynamics onto a Markov process defined over an exponentially large configuration space. Within this framework, quantum complexity arises from the proliferation of stochastic particles, which ultimately renders classical simulation and sampling intractable beyond a certain timescale. In the presence of noise, we demonstrate that for any unitary evolution generated by a linear combination of local or pairwise interactions, there exists at least one noise channel that effectively classicalizes the system by suppressing particle growth and making Monte Carlo sampling efficient. As a corollary, we show that for this class of unitaries, the dynamics of an open quantum spin chain subject to depolarizing noise undergoes an exact transition to classical simulability once the noise strength exceeds a critical threshold which can be efficiently determined for any model. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2604.19889 [quant-ph] (or arXiv:2604.19889v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.19889 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tony Jin [view email] [v1] Tue, 21 Apr 2026 18:11:19 UTC (1,012 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum-to-Classical Computability Transition via Negative Markov Chains, by Hugo L\'oio and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: cond-mat cond-mat.stat-mech 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?)