Artificial Neural Networks were recently shown to be an efficient representation of highly-entangled many-body quantum states. In practical applications, neural-network states inherit numerical schemes used in Variational Monte Carlo, most notably the use of Markov-Chain Monte-Carlo (MCMC) sampling to estimate quantum expectations. The local stochastic sampling in MCMC caps the potential advantages of neural networks in two ways: (i) Its intrinsic computational cost sets stringent practical limits on the width and depth of the networks, and therefore limits their expressive capacity; (ii) Its difficulty in generating precise and uncorrelated samples can result in estimations of observables that are very far from their true value. Inspired by the state-of-the-art generative models used in machine learning, we propose a specialized Neural Network architecture that supports efficient and exact sampling, completely circumventing the need for Markov Chain sampling. We demonstrate our approach for two-dimensional interacting spin models, showcasing the ability to obtain accurate results on larger system sizes than those currently accessible to neural-network quantum states.
Solving Statistical Mechanics Using Variational Autoregressive Networks
Peking University（北京大学）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Songshan Lake Materials Laboratory（松山湖材料实验室）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
Discrete Diffusion Models via Evolving Variational Autoregressive Networks
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学基础与前沿研究院）；School of Physics, University of Electronic Science and Technology of China（电子科技大学物理学院）；Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China（电子科技大学教育部量子物理与光子量子信息重点实验室）；Non-classical Information Science Basic Discipline Research Center of Sichuan Province, University of Electronic Science and Technology of China（电子科技大学四川省非经典信息科学基础学科研究中心）
Variational Autoregressive Networks with probability priors
Institute of Applied Computer Science, Jagiellonian University（贾科夫斯基大学应用计算机科学研究所）；Institute of Theoretical Physics, Jagiellonian University（贾科夫斯基大学理论物理研究所）
Entanglement and optimization within autoregressive neural quantum states
Institute for Theoretical Physics, ETH Zurich（苏黎世联邦理工学院理论物理研究所）；Vector Institute（向量研究所）；Politécnico Colombiano JIC（哥伦比亚JIC理工学院）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究院计算量子物理中心）
Variational Monte Carlo (VMC) with row-update Projected Entangled-Pair States (PEPS) and its applications in quantum spin glasses
Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China（中国科学技术大学现代物理系和微观尺度物理国家实验室）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）；School of Physical Science and Technology, Beijing University of Posts and Telecommunications（北京邮电大学物理科学与技术学院）；CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所理论物理重点实验室）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院基础物理与数学科学学院）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
