Learning Hidden Quantum Markov Models

TL;DR

This paper introduces a new learning algorithm for Hidden Quantum Markov Models (HQMMs), demonstrating that it can accurately learn HQMMs from synthetic data and outperform classical HMMs in terms of state efficiency.

Contribution

We extend HQMMs by showing how classical HMMs can be simulated on quantum circuits, relax constraints for modeling HMMs with HQMMs, and develop a learning algorithm for HQMM parameters.

Findings

The algorithm accurately learns HQMMs from synthetic data.

HQMMs require fewer hidden states than HMMs to achieve similar predictive accuracy.

The approach demonstrates potential for quantum probabilistic modeling of sequential data.

Abstract

Hidden Quantum Markov Models (HQMMs) can be thought of as quantum probabilistic graphical models that can model sequential data. We extend previous work on HQMMs with three contributions: (1) we show how classical hidden Markov models (HMMs) can be simulated on a quantum circuit, (2) we reformulate HQMMs by relaxing the constraints for modeling HMMs on quantum circuits, and (3) we present a learning algorithm to estimate the parameters of an HQMM from data. While our algorithm requires further optimization to handle larger datasets, we are able to evaluate our algorithm using several synthetic datasets. We show that on HQMM generated data, our algorithm learns HQMMs with the same number of hidden states and predictive accuracy as the true HQMMs, while HMMs learned with the Baum-Welch algorithm require more states to match the predictive accuracy.