Quantum Neural Network States: A Brief Review of Methods and Applications

作     者：Jia, Zhih-Ahn Yi, Biao Zhai, Rui Wu, Yu-Chun Guo, Guang-Can Guo, Guo-Ping 

作者机构：Key Laboratory of Quantum Information Chinese Academy of Sciences School of Physics University of Science and Technology of China Hefei Anhui230026 China CAS Center For Excellence in Quantum Information and Quantum Physics University of Science and Technology of China Hefei Anhui230026 China Microsoft Station Q Department of Mathematics University of California Santa BarbaraCA93106-6105 United States Department of Mathematics Capital Normal University Beijing100048 China Institute of Technical Physics Department of Engineering Physics Tsinghua University Beijing10084 China Origin Quantum Computing Hefei230026 China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2018年

核心收录：

主　　题：Neural networks 

摘      要：One of the main challenges of quantum many-body physics is the exponential growth in the dimensionality of the Hilbert space with system size. This growth makes solving the Schrödinger equation of the system extremely difficult. Nonetheless, many physical systems have a simplified internal structure that typically makes the parameters needed to characterize their ground states exponentially smaller. Many numerical methods then become available to capture the physics of the system. Among modern numerical techniques, neural networks, which show great power in approximating functions and extracting features of big data, are now attracting much interest. In this work, we briefly review the progress in using artificial neural networks to build quantum many-body states. We take the Boltzmann machine representation as a prototypical example to illustrate various aspects of the states of a neural network. We briefly review also the classical neural networks and illustrate how to use neural networks to represent quantum states and density operators. Some physical properties of the neural network states are discussed. For applications, we briefly review the progress in many-body calculations based on neural network states, the neural network state approach to tomography, and the classical simulation of quantum computing based on Boltzmann machine states. Copyright © 2018, The Authors. All rights reserved.