Learning Circular Hidden Quantum Markov Models: A Tensor Network Approach

TL;DR

This paper introduces circular Hidden Quantum Markov Models (c-HQMMs) that leverage tensor networks for efficient modeling of quantum and classical temporal data, demonstrating superior performance over existing models on real datasets.

Contribution

It presents a novel circular HQMM framework linked to tensor networks, enabling efficient learning and application to quantum and classical datasets.

Findings

c-HQMMs outperform traditional HQMMs and HMMs on multiple datasets

The tensor network approach provides an efficient learning method

c-HQMMs effectively model quantum temporal data

Abstract

In this paper, we propose circular Hidden Quantum Markov Models (c-HQMMs), which can be applied for modeling temporal data in quantum datasets (with classical datasets as a special case). We show that c-HQMMs are equivalent to a constrained tensor network (more precisely, circular Local Purified State with positive-semidefinite decomposition) model. This equivalence enables us to provide an efficient learning model for c-HQMMs. The proposed learning approach is evaluated on six real datasets and demonstrates the advantage of c-HQMMs on multiple datasets as compared to HQMMs, circular HMMs, and HMMs.