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

Xiao-Yu Li1, Qin-Sheng Zhu2, Yong Hu2, Hao Wu2,3, Guo-Wu Yang4, Lian-Hui Yu2, and Geng Chen4

1School of Information and Software Engineering, University of Electronic Science and Technology of China, Cheng Du, 610054, China
2School of Physics, University of Electronic Science and Technology of China, Cheng Du, 610054, China
3Institute of Electronics and Information Industry Technology of Kash, Kash, 844000, China
4School of Computer Science and Engineering, University of Electronic Science and Technology of China, Cheng Du, 610054, China

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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.

In this work, starting from the framework of open-system physical theory and utilizing the quantum condition master equation derived from the introduction of detailed balance conditions, we theoretically establish the connection between the quantum condition master equation and the quantum hidden Markov model. Simultaneously, we propose a novel Splitting Quantum Markov Model (SHQMM). Excitingly, experimental results not only validate the superiority of quantum algorithms over classical algorithms but also demonstrate that our model outperforms previous HQMMs, offering broad applications in the study of internal states of quantum systems.

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