Quantum Viterbi Algorithm

Quantum Physics arXiv:2605.18912 (quant-ph) [Submitted on 17 May 2026] Title:Quantum Viterbi Algorithm Authors:Luigi Accardi, Abdessatar Souissi, El Gheteb Soueidi, Farrukh Mukhamedov, Mohamed Rhaima View a PDF of the paper titled Quantum Viterbi Algorithm, by Luigi Accardi and 4 other authors View PDF HTML (experimental) Abstract:We introduce a quantum Viterbi decoding algorithm for hidden quantum Markov models (HQMMs) motivated by quantum information processing and quantum algorithms. Given a finite sequence of measurement outcomes, the algorithm identifies hidden quantum trajectories that maximize a joint decoding functional, serving as a genuine quantum analogue of the classical Viterbi score. Unlike classical hidden Markov models, where decoding optimizes over a finite discrete state space, our method performs optimization over a continuous manifold of pure quantum effects, thereby exploiting coherent superpositions in the hidden memory. We prove a strict quantum advantage: coherent hidden trajectories can achieve decoding scores that strictly exceed any classical strategy constrained to diagonal (commuting) effects, even when both models share the same observed statistics. These results position quantum Viterbi decoding as a concrete quantum algorithmic primitive for sequential decision-making, with direct applications to quantum memories, quantum communication with memory, and near-term quantum machine learning on NISQ devices. Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Probability (math.PR) Cite as: arXiv:2605.18912 [quant-ph] (or arXiv:2605.18912v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.18912 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Abdessatar Souissi [view email] [v1] Sun, 17 May 2026 20:09:26 UTC (32 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Viterbi Algorithm, by Luigi Accardi and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: math math-ph math.MP math.PR 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?)