A new quantum machine learning algorithm: split hidden quantum Markov model inspired by quantum conditional master equation

TL;DR

This paper introduces the split hidden quantum Markov model (SHQMM), a novel quantum machine learning algorithm inspired by the quantum conditional master equation, demonstrating improved robustness and applicability for analyzing quantum systems and time series.

Contribution

The paper presents a new SHQMM model and a related learning algorithm, advancing quantum machine learning by linking quantum transport systems to HQMMs and enhancing analysis capabilities.

Findings

SHQMM outperforms previous models in scope and robustness

Established a physical representation of HQMM using quantum transport systems

Provided algorithms for parameter learning in HQMMs

Abstract

The Hidden Quantum Markov Model (HQMM) has significant potential for analyzing time-series data and studying stochastic processes in the quantum domain as an upgrading option with potential advantages over classical Markov models. In this paper, we introduced the split HQMM (SHQMM) for implementing the hidden quantum Markov process, utilizing the conditional master equation with a fine balance condition to demonstrate the interconnections among the internal states of the quantum system. The experimental results suggest that our model outperforms previous models in terms of scope of applications and robustness. Additionally, we establish a new learning algorithm to solve parameters in HQMM by relating the quantum conditional master equation to the HQMM. Finally, our study provides clear evidence that the quantum transport system can be considered a physical representation of HQMM. The SHQMM with accompanying algorithms present a novel method to analyze quantum systems and time series grounded in physical implementation.