Based on the central limit theorem, we discuss the problem of evaluation of the statistical error of Monte Carlo calculations using a time discretized diffusion process. We present a robust and practical method to determine the effective variance of general observables and show how to verify the equilibrium hypothesis by the Kolmogorov-Smirnov test. We then derive scaling laws of the efficiency illustrated by Variational Monte Carlo calculations on the two dimensional electron gas.
Variational and Diffusion Quantum Monte Carlo Calculations with the CASINO Code
University of Cambridge（剑桥大学）；University College London（伦敦大学学院）；Lancaster University（兰开斯特大学）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）
Convergence of variational Monte Carlo simulation and scale-invariant pre-training
The Simons Institute for the Theory of Computing（西蒙斯理论计算研究所）；University of California, Berkeley（加利福尼亚大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
mVMC - Open-source software for many-variable variational Monte Carlo method
mVMC（many-variable Variational Monte Carlo）是一个基于变分蒙特卡罗方法的开源软件，适用于相互作用费米子系统的各种哈密顿量。在mVMC中，我们引入了超过一万个变参数，并同时优化他们使用随机重构（SR）方法。在本文中，我们解释mVMC的基础知识和用户界面。通过使用mVMC，用户可以通过为广泛研究的量子晶格模型准备大约十行的一个输入文件来执行计算，并且还可以通过准备几个额外的输入文件来执行一般的哈密顿量。我们展示了哈伯德模型、海森堡模型和近藤晶格模型的mVMC的基准结果。这些基准结果表明，mVMC提供的基态和低能激发态波函数相互作用费米子系统的高精度。
Monte Carlo Tree Search based Hybrid Optimization of Variational Quantum Circuits
University of California, Berkeley（加州大学伯克利分校）；Stanford University（斯坦福大学）；St. Kliment Ohridski University of Sofia（索非亚圣克里门特·奥赫里德大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo
Department of Physics；Astronomy, University of California, Davis, California 95616, USA；Astronomy, San Jos\'e State University, San Jos\'e, California 95192, USA；Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada；Vector Institute, Toronto, Ontario, M5G 0C6, Canada
