Stochastic resolution-of-the-identity auxiliary-field quantum Monte Carlo: Scaling reduction without overhead.

@article{Lee2020StochasticRA,
  title={Stochastic resolution-of-the-identity auxiliary-field quantum Monte Carlo: Scaling reduction without overhead.},
  author={Joonho Lee and David R. Reichman},
  journal={The Journal of chemical physics},
  year={2020},
  volume={153 4},
  pages={
          044131
        }
}
We explore the use of the stochastic resolution-of-the-identity (sRI) with the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) method. sRI is combined with four existing local energy evaluation strategies in ph-AFQMC, namely, (1) the half-rotated electron repulsion integral tensor (HR), (2) Cholesky decomposition (CD), (3) tensor hypercontraction (THC), or (4) low-rank factorization (LR). We demonstrate that HR-sRI achieves no scaling reduction, CD-sRI scales as O(N3), and THC-sRI and… 
9 Citations

Figures and Tables from this paper

A Localized-Orbital Energy Evaluation for Auxiliary-Field Quantum Monte Carlo.
Phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) has recently emerged as a promising method for the production of benchmark-level simulations of medium- to large-sized molecules because of
Selected configuration interaction wave functions in phaseless auxiliary field quantum Monte Carlo.
We present efficient algorithms for using selected configuration interaction (sCI) trial wave functions in phaseless auxiliary field quantum Monte Carlo (ph-AFQMC). These advances, geared toward
A phaseless auxiliary-field quantum Monte Carlo perspective on the uniform electron gas at finite temperatures: Issues, observations, and benchmark study.
TLDR
It is found that ph-FT-AFQMC exchange-correlation energies are in better agreement with a known parameterization than is restricted path-integral MC in the regime of Θ ≤ 0.5 and rs ≤ 2, which highlights the strength of ph- FT-AFZMC.
Frontiers of stochastic electronic structure calculations.
TLDR
This special issue of the Journal of Chemical Physics includes 33 papers that describe recent developments and applications in stochastic electronic structure methods, and can accurately describe systems with strong electron correlation.
Some recent developments in auxiliary-field quantum Monte Carlo for real materials.
TLDR
A systematic exposition of the key steps of AFQMC is given, closely tracking the framework of a modern software library the authors are developing and a self-consistent constraint for real materials is proposed.
Spectral Functions from Auxiliary-Field Quantum Monte Carlo without Analytic Continuation: The Extended Koopmans' Theorem Approach.
TLDR
It is found that EKT1-AFQMC can reproduce the qualitative features of spectral functions for Koopmans-like charge excitations with errors in peak locations of less than 0.25 eV in a finite basis.
Taming the Sign Problem in Auxiliary-Field Quantum Monte Carlo Using Accurate Wave Functions.
TLDR
This work adapts a recently proposed fast multi-Slater local energy evaluation algorithm for fp-AFQMC, making the use of long expansions from selected configuration interaction methods feasible and demonstrating how these wave functions serve to mitigate the sign problem and accelerate convergence in quantum chemical problems.
Taming the sign problem in auxiliary field quantum Monte Carlo using accurate trial wave functions
We explore different ways of incorporating accurate trial wave functions into free projection auxiliary field quantum Monte Carlo (fp-AFQMC). Trial states employed include coupled cluster singles and
The performance of phaseless auxiliary-field quantum Monte Carlo on the ground state electronic energy of benzene.
TLDR
The frozen core correlation energy of ph-AFQMC+RHF in thecc-pVTZ and cc-pVQZ basis sets as well as their complete basis set limit are reported.

References

SHOWING 1-10 OF 65 REFERENCES
Accelerating Auxiliary-Field Quantum Monte Carlo Simulations of Solids with Graphical Processing Units.
TLDR
This work outlines how auxiliary-field quantum Monte Carlo (AFQMC) can leverage graphical processing units (GPUs) to accelerate the simulation of solid state sytems and demonstrates the ability of AFQMC to systematically converge solid state calculations with respect to basis set and system size.
QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion quantum Monte Carlo.
TLDR
Recent advances in the capabilities of the open source ab initio Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus are reviewed and a new set of correlation-consistent effective core potentials (pseudopotentials) that are more accurate than previous sets are utilized.
Utilizing Essential Symmetry Breaking in Auxiliary-Field Quantum Monte Carlo: Application to the Spin Gaps of the C36 Fullerene and an Iron Porphyrin Model Complex.
TLDR
This work highlights the utility, scalability, and accuracy of ph-AFQMC with a single determinant trial wavefunction with essential symmetry breaking for systems mainly dominated by dynamical correlation with little static correlation.
An auxiliary-Field quantum Monte Carlo perspective on the ground state of the dense uniform electron gas: An investigation with Hartree-Fock trial wavefunctions
We assess the utility of spin-restricted Hartree-Fock (RHF) trial wavefunctions in performing phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) on the uniform electron gas (UEG) model. This
Efficient Ab Initio Auxiliary-Field Quantum Monte Carlo Calculations in Gaussian Bases via Low-Rank Tensor Decomposition.
TLDR
While the cost of conventional AFQMC calculations in Gaussian bases scales as O(N4) , it is shown that ground-state energies can be computed through tensor decomposition with reduced memory requirements and subquartic scaling.
Hamiltonian symmetries in auxiliary-field quantum Monte Carlo calculations for electronic structure
We describe how to incorporate symmetries of the Hamiltonian into auxiliary-field quantum Monte Carlo (AFQMC) calculations. Focusing on the case of Abelian symmetries, we show that the computational
Non-orthogonal multi-Slater determinant expansions in auxiliary field quantum Monte Carlo.
TLDR
The use of non-orthogonal multi-Slater determinant (NOMSD) expansions as trial wavefunctions in auxiliary field quantum Monte Carlo simulations of molecular systems are investigated and compare favorably with other accurate quantum many-body methods.
On Achieving High Accuracy in Quantum Chemical Calculations of 3 d Transition Metal-Containing Systems: A Comparison of Auxiliary-Field Quantum Monte Carlo with Coupled Cluster, Density Functional Theory, and Experiment for Diatomic Molecules.
TLDR
The ph-AFQMC method has tremendous potential, exhibiting unprecedented consistency and accuracy compared to other approximate quantum chemical approaches, and is found to give robust agreement with experiment superior to that of all other methods.
Overcoming the Memory Bottleneck in Auxiliary Field Quantum Monte Carlo Simulations with Interpolative Separable Density Fitting.
We investigate the use of interpolative separable density fitting (ISDF) as a means to reduce the memory bottleneck in auxiliary field quantum Monte Carlo (AFQMC) simulations of real materials in
Singlet-Triplet Energy Gaps of Organic Biradicals and Polyacenes with Auxiliary-Field Quantum Monte Carlo.
TLDR
It is shown that phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) can accurately predict singlet-triplet gaps for chemical systems with singlet states of highly biradical nature, including a set of 13 small molecules and the ortho-, meta-, and para- isomers of benzyne.
...
1
2
3
4
5
...