Quantum Dimension Reduction of Hidden Markov Models

Abstract

Hidden Markov models (HMMs) are ubiquitous in time-series modelling, with applications ranging from chemical reaction modelling to speech recognition. These HMMs are often large, with high-dimensional memories. A recently-proposed application of quantum technologies is to execute quantum analogues 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 \emph{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 favourable memory--accuracy trade-offs in the examples studied, relative to a simple classical state-merging baseline.

14 pages, 6 figures

References in corpus (26)

• Computational Mechanics: Pattern and Prediction, Structure and Simplicity
• Unsupervised Generative Modeling Using Matrix Product States
• Tangent-space methods for uniform matrix product states
• Occam's Quantum Razor: How Quantum Mechanics can reduce the complexity of classical models
• Learning Relevant Features of Data with Multi-scale Tensor Networks
• A practical, unitary simulator for non-Markovian complex processes
• Experimental quantum processing enhancement in modelling stochastic processes
• Extreme dimensionality reduction with quantum modelling
• A Closed-Form Shave from Occam's Quantum Razor: Exact Results for Quantum Compression
• Optimal stochastic modelling with unitary quantum dynamics
• A Hidden Markov Model of atomic quantum jump dynamics in an optically probed cavity
• Extreme Quantum Advantage for Rare-Event Sampling
• Superior memory efficiency of quantum devices for the simulation of continuous-time stochastic processes
• Unbounded memory advantage in stochastic simulation using quantum mechanics
• Matrix Product States for Quantum Stochastic Modelling
• Interfering trajectories in experimental quantum-enhanced stochastic simulation
• Quantum learning of classical stochastic processes: The Completely-Positive Realization Problem
• Memory compression and thermal efficiency of quantum implementations of non-deterministic hidden Markov models
• Single-shot quantum memory advantage in the simulation of stochastic processes
• Memory-efficient tracking of complex temporal and symbolic dynamics with quantum simulators
• Implementing quantum dimensionality reduction for non-Markovian stochastic simulation
• Prediction and Generation of Binary Markov Processes: Can a Finite-State Fox Catch a Markov Mouse?
• Quantum coarse-graining for extreme dimension reduction in modelling stochastic temporal dynamics
• Accuracy vs Memory Advantage in the Quantum Simulation of Stochastic Processes
• Embedding memory-efficient stochastic simulators as quantum trajectories
• Quantum theory in finite dimension cannot explain every general process with finite memory