Quantum-inspired Machine Learning with Hidden Quantum Markov Models and Tensor Networks

Abstract

The prospect of blending ideas from quantum information and machine learning has garnered interest in recent years, driven by their shared mathematical foundations in linear algebra and probability. A common way to categorize the research directions in this space is in terms of the goals (whether they are tackling classical or quantum problems) and methods (whether they rely on quantum-inspired classical computation or quantum computation). This work focuses on the potential of quantum-inspired classical machine learning approaches for solving select classical and quantum problems. In particular, we present our work on three main topics: (1) our formulation and learning algorithm for hidden quantum Markov models (HQMMs), a quantum-inspired analogue of hidden Markov models (HMMs) with greater expressiveness and without the learning challenges associated with previous proposals extending HMMs, (2) the connection between HQMMs (and similar proposals) and tensor networks, a general and tractable classical method for approximating high-dimensional classical and quantum systems with unfavorable scaling, and (3) our scalable implementation of 'iterative Bayesian unfolding', an expectation-maximization algorithm for quantum measurement error mitigation, the problem of post-processing results from a quantum computer to account for measurement errors.