Quantum Algorithm for Numerical Energy Gradient Calculations at the Full Configuration Interaction Level of Theory

A Bayesian phase difference estimation (BPDE) algorithm allows us to compute the energy gap of two electronic states of a given Hamiltonian directly by utilizing the quantum superposition of their wave functions. Here we report an extension of the BPDE algorithm to the direct calculation of the energy difference of two molecular geometries. We apply the BPDE algorithm for the calculation of numerical energy gradients based on the two-point finite-difference method, enabling us to execute geometry optimization of one-dimensional molecules at the full-CI level on a quantum computer. Results of numerical quantum circuit simulations of the geometry optimization of the H-2 molecule with the STO-3G and 6-31G basis sets, the LiH and BeH2 molecules at the full-CI/STO-3G level, and the N-2 molecule at the CASCI(6e,6o)/6-311G* level are given.

Automated summary

In this paper, we extend the Bayesian phase difference estimation (BPDE) algorithm to calculate the energy difference of two molecular geometries directly. By applying the BPDE algorithm with numerical energy gradients based on the finite-difference method, we demonstrate the feasibility of geometry optimization of one-dimensional molecules on a quantum computer. Simulations of various molecular systems validate the effectiveness of the proposed method.