Physica Scripta

Quantum algorithm for Markov random fields structure learning

Liming Zhao, Ming-Xing Luo, Lin‐Chun Wan

Published Jun 26, 2025• 1 citation

Abstract

Abstract Probabilistic graphical models play a crucial role in machine learning and have wide applications across various fields. A pivotal subset within this realm is undirected graphical models, also known as Markov random fields. In this work, we explore the application of quantum computing to the field of machine learning, specifically focusing on the task of structure learning in Markov random fields. We propose a quantum algorithm for structure learning of an r-wise Markov Random Field with a bounded degree underlying graph, based on a nearly optimal classical greedy algorithm. Our quantum algorithm provides a polynomial speed-up over the classical counterpart, with a runtime of O ˜ 2 L M n r + 1 log ( 1 / w ) compared to the classical O ˜ M n r , where n is the number of variables. It is nearly a quadratic speedup in terms of n. Through this research, we aim to showcase the potential advantages of quantum computation in tackling complex machine-learning problems. Furthermore, the sample complexity O ˜ 2 2 L τ 2 δ 2 L ( log ( 1 / w ) + log n ) remains consistent between classical and quantum approaches, ensuring the efficiency and robustness of our method. By demonstrating the efficiency and scalability of our quantum algorithm for structure learning, we contribute to the growing body of work that highlights the role of quantum computing in advancing the field of machine learning and probabilistic graphical models.

DOI: 10.1088/1402-4896/ade8b5

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