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

Area of Science:

• Quantum Computing
• Computational Chemistry
• Quantum Algorithms

Background:

• The Bayesian phase difference estimation (BPDE) algorithm enables direct computation of energy gaps between electronic states using quantum superposition.
• Calculating energy differences between molecular geometries is crucial for understanding molecular behavior and chemical reactions.

Purpose of the Study:

• To extend the BPDE algorithm for the direct calculation of energy differences between two molecular geometries.
• To apply the extended BPDE algorithm for quantum-assisted molecular geometry optimization.

Main Methods:

• Extension of the BPDE algorithm to calculate energy differences for distinct molecular geometries.
• Application of the two-point finite-difference method for numerical energy gradient calculations.
• Full configuration interaction (full-CI) calculations performed on a quantum computer.

Main Results:

• Successful numerical quantum circuit simulations of geometry optimization for various molecules (H2, LiH, BeH2, N2).
• Demonstrated feasibility of full-CI level geometry optimization for 1D molecules using the extended BPDE algorithm.
• Validation of the approach using different basis sets (STO-3G, 6-31G, 6-311G*) and active space configurations (CASCI(6e,6o)).

Conclusions:

• The extended BPDE algorithm provides a direct and efficient method for calculating molecular energy differences and performing geometry optimizations on quantum computers.
• This work paves the way for more complex quantum computational chemistry applications, including accurate molecular structure determination.