State-dependent Trotter Limits and their approximations

Understand

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.