Quantifying noise tolerance of arbitrary Trotterized quantum simulation algorithms

Trotterization is a ubiquitous technique for implementing Hamiltonian simulation algorithms on digital quantum devices. Reducing Trotter error and achieving accurate simulation relies on implementing a significant number of Trotter steps, accomplished through repeated gate sequence applications. On noisy quantum devices this introduces a trade-off between the reduction in Trotter error and noise arising from the growth in circuit depth. We quantify this trade-off for Trotterized algorithms of arbitrary circuit depth subject to Markovian noise channels and determine a scalable threshold for algorithm noise tolerance. We explore how this threshold can be increased by error mitigation strategies in hybrid quantum-classical algorithms.