Bayesian phase difference estimation algorithm for direct calculation of fine structure splitting: accelerated simulation of relativistic and quantum many-body effects

TL;DR

This paper demonstrates a quantum algorithm, Bayesian Phase Difference Estimation, for accurately calculating fine-structure splittings in atomic systems, including superheavy ions, with significant speedup using GPU acceleration.

Contribution

It applies the BPDE quantum algorithm within the Dirac--Coulomb--Breit framework to predict atomic fine-structure splittings, covering a wide range of elements with high accuracy.

Findings

Predicts fine-structure splittings within 605.3 cm$^{-1}$ RMS deviation from experiments.

Achieves a 42.7-fold speedup using GPU acceleration compared to CPU.

Successfully simulates relativistic and electron correlation effects in atomic systems.

Abstract

Despite rapid progress in the development of quantum algorithms in quantum computing as well as numerical simulation methods in classical computing for atomic and molecular applications, no systematic and comprehensive electronic structure study of atomic systems that covers almost all of the elements in the periodic table using a single quantum algorithm has been reported. In this work, we address this gap by implementing the recently-proposed quantum algorithm, the Bayesian Phase Difference Estimation (BPDE) approach, to compute accurately fine-structure splittings, which are relativistic in origin and it also depends on quantum many-body (electron correlation) effects, of appropriately chosen states of atomic systems, including highly-charged superheavy ions. Our numerical simulations reveal that the BPDE algorithm, in the Dirac--Coulomb--Breit framework, can predict the fine-structure splitting of Boron-like ions to within 605.3 cm$^{-1}$ of root mean square deviations from the experimental ones, in the (1s, 2s, 2p, 3s, 3p) active space. We performed our simulations of relativistic and electron correlation effects on Graphics Processing Unit (GPU) by utilizing NVIDIA's cuQuantum, and observe a $\times 42.7$ speedup as compared to the CPU-only simulations in an 18-qubit active space.