Optimized Implementation for Calculation and Fast-Update of Pfaffians Installed to the Open-Source Fermionic Variational Solver mVMC

TL;DR

This paper introduces a high-performance, portable implementation for efficiently computing and updating Pfaffians and their inverses, significantly enhancing the sampling speed in fermionic variational Monte Carlo simulations.

Contribution

It presents a novel, optimized algorithm for Pfaffian calculations integrated into mVMC, improving performance across various processors without altering the sampling process.

Findings

Sampling performance increased by over 6 times

Implementation compatible with multiple modern processors

Enhanced efficiency in fermionic variational Monte Carlo

Abstract

In this article, we present a high performance, portable and well templated implementation for computing and fast-updating Pfaffian and inverse of an even-ranked skew-symmetric (antisymmetric) matrix. It is achieved with a skew-symmetric, blocked variant of the Parlett-Reid algorithm and a blocked update scheme based on the Woodbury matrix identity. Installation of this framework into the geminal-wavefunction-based many-variable Variational Monte Carlo (mVMC) code boosts sampling performance to up to more than $6$ times without changing Markov chain's behavior. The implementation is based on an extension of the BLAS-like instantiation software (BLIS) framework which has optimized kernel for many state-of-the-art processors including Intel Skylake-X, AMD EPYC Rome and Fujitsu A64FX.