A Hybrid Quantum-Classical Molecular Force Calculator (VQE-F) Integrated with Atomic Simulation Environment (ASE) for Molecular Geometry Optimization

To trace accurately the chemical reaction pathway of molecules, one requires accurate determination of the equilibrium or lowest energy molecular geometry, by computing energy gradients with respect to molecule’s nuclear coordinates or perturbatively distort the nuclear configuration to find the minimum energy configuration. In this work, we present a modular quantum-classical hybrid framework for molecular geometry optimization. We report here for the first-time an interface for the Variational Quantum Eigensolver (VQE) based Energy (VQE-E) and Force (VQE-F) calculation, to the classical computational Atomic Simulation Environment (ASE). ASE is a widely used open-source suite of Python modules for ab-initio atomistic simulation towards molecular geometry optimization and molecular dynamics. We used a finite-difference based, nested numerical differentiation technique to compute the atomic forces where the energy is obtained from the VQE algorithm. The working of this hybrid quantum-classical interface is demonstrated by optimizing the geometry of water molecule in different molecular orbital basis sets, which demonstrated a trade-off between computational accuracy and quantum circuit complexity. The calculator can further be configured to select different active space transformations, trial state ansatzes, fermion to qubit mappings and classical optimizers in the VQE workflow, for efficient and accurate estimates of molecular geometry.