Hashing algorithms, optimized mappings and massive parallelization of multiconfigurational methods for bosons

TL;DR

This paper develops efficient numerical routines for handling multiconfigurational bosonic states, introducing a hashing function, optimizing creation/annihilation operations, and leveraging GPU parallelization to significantly accelerate large-scale quantum many-body calculations.

Contribution

It introduces a novel hashing method for configuration indexing, improves operator conversion routines, and demonstrates massive parallelization with CUDA for scalable bosonic simulations.

Findings

Hashing function unambiguously maps configurations to indices

CUDA implementation achieves ~50x speedup over CPU

Validated with Lieb-Liniger gas ground state calculations

Abstract

Numerical routines for Fock states indexing and to handle creation and annihilation operators in the spanned multiconfigurational space are developed. From the combinatorial problem of fitting particles in a truncated basis of individual particle states, which defines the spanned multiconfigurational space, a hashing function is provided based on a metric to sort all possible configurations, which refers to sets of occupation numbers required in the definition of Fock states. Despite the hashing function unambiguously relates the configuration to the coefficient index of the many-particle state expansion in the Fock basis, averages of creation and annihilation operators can be a highly demanding computation, especially when they are embedded in a time-dependent problem. Therefore, improvements in the conversion between configurations after the action of creation and annihilation operators are thoroughly inspected, highlighting the advantages and additional memory consumption. We also exploit massive parallel processors from graphics processor units with CUDA to improve a routine to act with the many-body Hamiltonian matrix on the spanned multiconfigurational space, which demonstrated quantitatively the scalability of the problem. The improvements shown here seem promising especially for calculations involving a large number of particles, in which case, the optimized CUDA code provided a drastic performance gain of roughly fifty times faster than a single core processor. The codes were consistently tested with an application to the Lieb-Liniger gas, evaluating the ground state and comparing with the analytical solution.