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Despite rapid progress in the development of quantum algorithms in quantumcomputing as well as numerical simulation methods in classical computing foratomic and molecular applications, no systematic and comprehensive electronicstructure study of atomic systems that covers almost all of the elements in theperiodic table using a single quantum algorithm has been reported. In thiswork, we address this gap by implementing the recently-proposed quantumalgorithm, the Bayesian Phase Difference Estimation (BPDE) approach, to computeaccurately fine-structure splittings, which are relativistic in origin and italso depends on quantum many-body (electron correlation) effects, ofappropriately chosen states of atomic systems, including highly-chargedsuperheavy ions. Our numerical simulations reveal that the BPDE algorithm, inthe Dirac--Coulomb--Breit framework, can predict the fine-structure splittingof Boron-like ions to within 605.3 cm$^{-1}$ of root mean square deviationsfrom the experimental ones, in the (1s, 2s, 2p, 3s, 3p) active space. Weperformed our simulations of relativistic and electron correlation effects onGraphics 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-qubitactive space.

electronic structure

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