Hidden Quantum Markov Models with one qubit

TL;DR

This paper compares 1-bit Hidden Markov Models and 1-qubit Hidden Quantum Markov Models, demonstrating that HQMMs can generate stronger correlations despite similar resource requirements.

Contribution

It provides a comparative analysis showing that 1-qubit HQMMs can produce stronger correlations than classical 1-bit HMMs, highlighting quantum advantages.

Findings

HQMMs produce stronger correlations than HMMs.

Both models are comparable in resource usage.

Quantum models can enhance sequential data analysis.

Abstract

Hidden Markov Models (HMMs) have become very popular as a computational tool for the analysis of sequential data. They are memoryless machines which transition from one internal state to another, while producing symbols. These symbols constitute the output of the machine and form an infinite time series. Analogously, Hidden Quantum Markov Models (HQMM) produce an infinite time series, while progressing from one quantum state to another through stochastic quantum operations. Here we compare 1-bit HMMs and 1-qubit HQMMs and show that the latter can produce stronger correlations, although both machines are, in principle, comparable in resources.