2020/10/20 by Siddarth Srinivasan, Sandesh Adhikary, Srinivasan, Siddarth +7 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum many-body systems #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2010.10653
openalex publication_date 2020/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to tractably model many-body systems. But similar models have also been studied in the stochastic processes and weighted automata literature, with little work on how these bodies of work relate to each other. We address this gap by showing how stationary or uniform versions of popular quantum tensor network models have equivalent representations in the stochastic processes and weighted automata literature, in the limit of infinitely long sequences. We demonstrate several equivalence results between models used in these three communities: (i) uniform variants of matrix product states, Born machines and locally purified states from the quantum tensor networks literature, (ii) predictive state representations, hidden Markov models, norm-observable operator models and hidden quantum Markov models from the stochastic process literature,and (iii) stochastic weighted automata, probabilistic automata and quadratic automata from the formal languages literature. Such connections may open the door for results and methods developed in one area to be applied in another.