We present an overview of the variational and diffusion quantum Monte Carlo methods as implemented in the CASINO program. We particularly focus on developments made in the last decade, describing state-of-the-art quantum Monte Carlo algorithms and software and discussing their strengths and their weaknesses. We review a range of recent applications of CASINO.
The introduction of Neural Quantum States (NQS) has recently given a new twist to variational Monte Carlo (VMC). The ability to systematically reduce the bias of the wave function ansatz renders the approach widely applicable. However, performant implementations are crucial to reach the numerical state of the art. Here, we present a Python codebase that supports arbitrary NQS architectures and model Hamiltonians. Additionally leveraging automatic differentiation, just-in-time compilation to accelerators, and distributed computing, it is designed to facilitate the composition of efficient NQS a…
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）
Rydberg atom arrays are programmable quantum simulators capable of preparing interacting qubit systems in a variety of quantum states. Due to long experimental preparation times, obtaining projective measurement data can be relatively slow for large arrays, which poses a challenge for state reconstruction methods such as tomography. Today, novel groundstate wavefunction ansätze like recurrent neural networks (RNNs) can be efficiently trained not only from projective measurement data, but also through Hamiltonian-guided variational Monte Carlo (VMC). In this paper, we demonstrate how pretrainin…
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。
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here, we develop a variational approach for solving partial differential equations governing the evolution of high dimensional probability distributions. Our approach naturally works on the unbounded continuous domain and encodes the full probability density function through its variational parameters, which are adapted dynamically during the evolution to optimally…
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）
Variational quantum algorithms stand at the forefront of simulations on near-term and future fault-tolerant quantum devices. While most variational quantum algorithms involve only continuous optimization variables, the representational power of the variational ansatz can sometimes be significantly enhanced by adding certain discrete optimization variables, as is exemplified by the generalized quantum approximate optimization algorithm (QAOA). However, the hybrid discrete-continuous optimization problem in the generalized QAOA poses a challenge to the optimization. We propose a new algorithm ca…
Obtaining accurate ground and low-lying excited states of electronic systems is crucial in a multitude of important applications. One ab initio method for solving the Schrödinger equation that scales favorably for large systems is variational quantum Monte Carlo (QMC). The recently introduced deep QMC approach uses ansatzes represented by deep neural networks and generates nearly exact ground-state solutions for molecules containing up to a few dozen electrons, with the potential to scale to much larger systems where other highly accurate methods are not feasible. In this paper, we extend one …
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
