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

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 determine fine structure splittings of a wide range of boron-like atomic systems. Since accurate estimate of fine structure splittings strongly depend on the relativistic as well as quantum many-body effects, our study can test the potential of the BPDE approach to produce results close to the experimental values. Our numerical simulations reveal that the BPDE algorithm, in the Dirac–Coulomb–Breit framework, can predict fine structure splittings of ground states of the considered systems quite precisely. We performed our simulations of relativistic and electron correlation effects on Graphics Processing Unit by utilizing NVIDIA’s cuQuantum, and observe a ×42.7 speedup as compared to the Central Processing Unit-only simulations in an 18-qubit active space.