Learning Quantum-Samplers for Stochastic Processes with Quantum Sequence Models

Quantum Physics [Submitted on 25 Mar 2026] Learning Quantum-Samplers for Stochastic Processes with Quantum Sequence Models Ximing Wang, Chengran Yang, Chidambaram Aditya Somasundaram, Jayne Thompson, Mile Gu Quantum circuits that generate coherent superpositions of stochastic processes are key to many downstream quantum-accelerated tasks, such as risk analysis, importance sampling, and DNA sequencing. However, traditional methods for designing such circuits from data face immense challenges, given the exponential growth in the size of the associated probability vectors as the desired simulation time horizon increases. Here, we introduce quantum sequence models that leverage a recurrent quantum circuit structure to generate coherent superpositions with circuit complexity that grows linearly with the desired time horizon; together with a recurrent variant of the parameter-shift rule, we train these models from observational data. When benchmarked against baseline quantum Born machines, our constructions exhibit orders-of-magnitude improvements in model accuracy in data-sparse regimes. Comments: 12 pages, 6 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.24069 [quant-ph]   (or arXiv:2603.24069v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.24069 Focus to learn more Submission history From: Ximing Wang [view email] [v1] Wed, 25 Mar 2026 08:23:56 UTC (2,496 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)