State-dependent Trotter Limits and their approximations

TL;DR

This paper establishes conditions and explicit bounds for the validity of discretized quantum simulations using Trotter product formulas, focusing on state-dependent errors crucial for accurate numerical modeling.

Contribution

It introduces sufficient conditions and explicit bounds for state-dependent Trotter errors, enhancing the reliability of discretized quantum simulations.

Findings

Derived explicit bounds for Trotter errors based on quantum states

Provided criteria for the validity of discretized quantum models

Enhanced understanding of state-dependent errors in quantum simulations

Abstract

The Trotter product formula is a key instrument in numerical simulations of quantum systems. However, computers cannot deal with continuous degrees of freedom, such as the position of particles in molecules, or the amplitude of electromagnetic fields. It is therefore necessary to discretize these variables to make them amenable to digital simulations. Here, we give sufficient conditions to conclude the validity of this approximate discretized physics. Essentially, it depends on the state-dependent Trotter error, for which we establish explicit bounds that are also of independent interest.