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Quantum dimension reduction of hidden Markov models

Rishi Sundar1,2 and Thomas J. Elliott1,3,2

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Phys. Rev. A 113, 062461 – Published 25 June, 2026

DOI: https://doi.org/10.1103/plt9-cm1x

Abstract

Hidden Markov models (HMMs) are ubiquitous in time-series modeling, with applications ranging from chemical reaction modeling to speech recognition. These HMMs are often large, with high-dimensional memories. A recently proposed application of quantum technologies is to execute quantum analogs of HMMs. Such quantum HMMs (QHMMs) are strictly more expressive than their classical counterparts, enabling the construction of more parsimonious models of stochastic processes. However, state-of-the-art techniques for QHMM compression, based on tensor networks, are only applicable for a restricted subset of HMMs, where the transitions are deterministic. In this work we introduce a pipeline by which any finite, ergodic HMM can be compressed in this manner, providing a route for effective quantum dimension reduction of general HMMs. We demonstrate the method on both a simple toy model, and on a speech-derived HMM trained from data, obtaining favorable memory-accuracy tradeoffs in the examples studied, relative to a simple classical state-merging baseline.

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Phys. Rev. A 113, 062461– Published 25 June, 2026
  • Received 23 January 2026
  • Revised 30 March 2026
  • Accepted 12 May 2026
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