Neural networks can be used to identify phases and phase transitions in
condensed matter systems via supervised machine learning. Readily programmable
through modern software libraries, we show that a standard feed-forward neural
network can be trained to detect multiple types of order parameter directly
from raw state configurations sampled with Monte Carlo. In addition, they can
detect highly non-trivial states such as Coulomb phases, and if modified to a
convolutional neural network, topological phases with no conventional order
parameter. We show that this classification occurs within the neural network
without knowledge of the Hamiltonian or even the general locality of
interactions. These results demonstrate the power of machine learning as a
basic research tool in the field of condensed matter and statistical physics.

采用神经网络通过监督学习来识别凝聚态系统中的相和相变，能够通过现代软件库方便地进行编程，能够检测到多种类型的序参量，包括高度非平凡的库仑相，并且即使在没有哈密顿量甚至相互作用的广义局部性知识下，也能够实现分类。

机器学习物态相

Machine learning phases of matter

The curse of dimensionality associated with the Hilbert space of spin systems
provides a significant obstruction to the study of condensed matter systems.
Tensor networks have proven an important tool in attempting to overcome this
difficulty in both the numerical and analytic regimes.
These notes form the basis for a seven lecture course, introducing the basics
of a range of common tensor networks and algorithms. In particular, we cover:
introductory tensor network notation, applications to quantum information,
basic properties of matrix product states, a classification of quantum phases
using tensor networks, algorithms for finding matrix product states, basic
properties of projected entangled pair states, and multiscale entanglement
renormalisation ansatz states.
The lectures are intended to be generally accessible, although the relevance
of many of the examples may be lost on students without a background in
many-body physics/quantum information. For each lecture, several problems are
given, with worked solutions in an ancillary file.

这篇论文介绍了一种克服 Hilbert 空间维度问题的重要工具 —— 张量网络，同时涵盖了基本张量网络和算法的介绍，以及其在量子信息中的应用，包括矩阵乘积状态、基本性质、基于张量网络的量子相分类、寻找矩阵乘积状态算法、基于投影纠缠对状态的基本性质和多尺度纠缠重整化阈址状态。