Twenty Years of Auxiliary-Field Quantum Monte Carlo in Quantum Chemistry: An Overview and Assessment on Main Group Chemistry and Bond-Breaking

Abstract

In this work, we present an overview of the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) approach from a computational quantum chemistry perspective and present a numerical assessment of its performance on main group chemistry and bond-breaking problems with a total of 1004 relative energies. While our benchmark study is somewhat limited, we make recommendations for the use of ph-AFQMC for general main-group chemistry applications. For systems where single determinant wave functions are qualitatively accurate, we expect the accuracy of ph-AFQMC in conjunction with a single-determinant trial wave function to be between that of coupled-cluster with singles and doubles (CCSD) and CCSD with perturbative triples (CCSD(T)). For these applications, ph-AFQMC should be a method of choice when canonical CCSD(T) is too expensive to run. For systems where multireference (MR) wave functions are needed for qualitative accuracy, ph-AFQMC is far more accurate than MR perturbation theory methods and competitive with MR configuration interaction (MRCI) methods. Due to the computational efficiency of ph-AFQMC compared to MRCI, we recommended ph-AFQMC as a method of choice for handling dynamic correlation in MR problems. We conclude with a discussion of important directions for future development of the ph-AFQMC approach.

Data-Efficient Machine Learning Potentials from Transfer Learning of Periodic Correlated Electronic Structure Methods: Liquid Water at AFQMC, CCSD, and CCSD(T) Accuracy

“…In this work, we employ the simplest trial wave function, the spin-restricted Hartree–Fock determinant. A recent benchmark study examined the accuracy of AFQMC with Hartree–Fock trial wave functions over 1004 data points, and based on these results at this level of approximation, we expect the accuracy of AFQMC to be between CCSD and CCSD­(T) for the problems considered here.…”

Bootstrap Embedding on a Quantum Computer

“…Alternately, different flavors of stochastic electronic structure solvers can be employed as fragment solvers in BE. Depending on implementation, these stochastic solvers can be biased or unbiased (if unbiased, with a cost of introducing the phase problem in general). − Collecting each sample on a classical computer usually has similar cost as a mean field theory (roughly O ( N 3 )), while the overall target accuracy ϵ on observable estimation can be achieved with a sampling overhead of roughly O ( 1 ϵ 2 ) with a constant prefactor depending on the severity of the sign problem.…”

“…Depending on implementation, these stochastic solvers can be biased or unbiased (if unbiased, with a cost of introducing the phase problem in general). 60 with a constant prefactor depending on the severity of the sign problem. Importantly, the sampling feature of these stochastic electronic structure methods on classical computers are strikingly similar to the nature of quantum computers where measurement necessarily collapses the wave function.…”

ipie: A Python-Based Auxiliary-Field Quantum Monte Carlo Program with Flexibility and Efficiency on CPUs and GPUs

“…In this paper, we hope to focus more on the computational and implementational aspects of ph-AFQMC as relevant to . We will only summarize the essence of AFQMC, so interested readers are referred to recent ph-AFQMC reviews ,,, for more theoretical details on ph-AFQMC.…”

“…AFQMC has proven to be one of the more promising approaches to many-electron correlation problems. − Historically, the method has been mostly applied to lattice models within the constrained path approximation, but there has been an increasing interest in applying this method within the phaseless approximation to ab initio systems. ,,, Despite its success, the open-source code development has seen rather slow progress until recently although a proof-of-concept implementation in was available for the Hubbard model in 2014. For ab initio systems, it was only within the last 10 years when the first production-level, open-source implementation developed by Morales and co-workers in appeared. , Since then, another proof-of-concept program, , written in Python by Malone and Lee, was made available.…”