Variationally Compressing Quantum Circuits to Approximate Nonadiabatic Molecular Quantum Dynamics

Abstract

Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably approximating deep circuits representing potential landscapes becomes crucial for simulating real quantum systems. Variationally approximating unitaries allows for shallower circuits and accuracy tunable to hardware fidelity, so long as the observable quantities are preserved. We show the variational compression of Trotter terms preserve reaction rate coefficients via classical emulation of a hybrid quantum-classical optimization method, as well as fast-forwarded adiabatic dynamics on quantum hardware. Compressed circuits can be incorporated with product-formula-based time evolution to approximate dynamics of a particle in two coupled harmonic potentials, allowing tunability when removing high-cost qubit interactions. Approximate rate coefficients are recovered after substituting terms in a nonadiabatic dynamic process, giving proof-of-principle for observable preservation under variational optimization. Attention is paid to minimizing qubit and gate-count resources.