Digital quantum simulation of controlled molecular dynamics in first quantization

A longstanding goal is to use laser fields to coherently control the dynamics of quantum systems, such as atoms and molecules. In pursuit of this goal, simulations are essential for designing laser fields that achieve a desired control outcome. In this talk, we investigate the viability of quantum computers for performing these simulations in the presence of low-probability logical errors. We specifically consider simulating controlled molecular dynamics on quantum computers using Trotterized, time-dependent Hamiltonian simulation algorithms within a grid-based, first-quantized representation. We discuss the algorithm formulation, its asymptotic costs, and its compilation into Clifford + T gates. We then present numerical results for simulations of a controlled hydrogenic system. These numerical illustrations explore the impact of uncorrected logical errors, as well as Trotter error, on the simulation outcomes.