The use of artificial neural networks to represent quantum wave-functions has
recently attracted interest as a way to solve complex many-body problems. The
potential of these variational parameterizations has been supported by
analytical and numerical evidence in controlled benchmarks. While approaching
the end of the early research phase in this field, it becomes increasingly
important to show how neural-network states perform for models and physical
problems that constitute a clear open challenge for other many-body
computational methods. In this paper we start addressing this aspect,
concentrating on a presently unsolved model describing two-dimensional
frustrated magnets. Using a fully convolutional neural network model as a
variational ansatz, we study the frustrated spin-1/2 J1-J2 Heisenberg model on
the square lattice. We demonstrate that the resulting predictions for both
ground-state energies and properties are competitive with, and often improve
upon, existing state-of-the-art methods. In a relatively small region in the
parameter space, corresponding to the maximally frustrated regime, our ansatz
exhibits comparatively good but not best performance. The gap between the
complexity of the models adopted here and those routinely adopted in deep
learning applications is, however, still substantial, such that further
improvements in future generations of neural-network quantum states are likely
to be expected.

使用卷积神经网络模型作为变分 ansatz，研究了二维受挫磁体的模型，证明了所得结果与现有的最先进方法相当甚至更好。

利用神经网络量子态研究二维受阻 J1-J2 模型

Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network  Quantum States

The variational method is a versatile tool for classical simulation of a
variety of quantum systems. Great efforts have recently been devoted to its
extension to quantum computing for efficiently solving static many-body
problems and simulating real and imaginary time dynamics. In this work, we
first review the conventional variational principles, including the
Rayleigh-Ritz method for solving static problems, and the Dirac and Frenkel
variational principle, the McLachlan's variational principle, and the
time-dependent variational principle, for simulating real time dynamics. We
focus on the simulation of dynamics and discuss the connections of the three
variational principles. Previous works mainly focus on the unitary evolution of
pure states. In this work, we introduce variational quantum simulation of mixed
states under general stochastic evolution. We show how the results can be
reduced to the pure state case with a correction term that takes accounts of
global phase alignment. For variational simulation of imaginary time evolution,
we also extend it to the mixed state scenario and discuss variational Gibbs
state preparation. We further elaborate on the design of ansatz that is
compatible with post-selection measurement and the implementation of the
generalised variational algorithms with quantum circuits. Our work completes
the theory of variational quantum simulation of general real and imaginary time
evolution and it is applicable to near-term quantum hardware.

本文介绍了变分原理的应用，包括用于解决静态问题的 Rayleigh-Ritz 方法，以及用于模拟实时动力学的 Dirac、Frenkel 和 McLachlan 变分原理。同时，本文还形容了它们之间的联系，并进一步扩展了变分方法以适应混合态干扰，包括虚时间和实时间的模拟，并设计了用于量子电路的变分算法。