Mixed quantum-classical dynamics for near term quantum computers

Mixed quantum-classical dynamics is a set of methods often used to understand systems too complex to treat fully quantum mechanically. Many techniques exist for full quantum mechanical evolution on quantum computers, but mixed quantum-classical dynamics are less explored. We present a modular algorithm for general mixed quantum-classical dynamics where the quantum subsystem is coupled with the classical subsystem. We test it on a modified Shin-Metiu model in the first quantization through Ehrenfest propagation. We find that the Time-Dependent Variational Time Propagation algorithm performs well for short-time evolutions and retains qualitative results for longer-time evolutions. The full-quantum propagation of molecular degrees of freedom is onerous even for the capability of noisy intermediate-scale quantum devices (NISQ), and methods to perform mixed quantum-classical dynamics on NISQ devices are at an early stage of development. The authors present a modular algorithm to perform mixed quantum-classical dynamics NISQ devices.