State-dependent Trotter Limits and their approximations

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.

16 pages, 5 figures

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Cited by in corpus (9)

• Strong Error Bounds for Trotter & Strang-Splittings and Their Implications for Quantum Chemistry
• Complexity of Digital Quantum Simulation in the Low-Energy Subspace: Applications and a Lower Bound
• Lower Bounds for the Trotter Error
• Trotterization is substantially efficient for low-energy states
• Convergence of Dynamics on Inductive Systems of Banach Spaces
• Energy-limited quantum dynamics
• Faster Algorithmic Quantum and Classical Simulations by Corrected Product Formulas
• Convergence Rates for the Trotter Splitting for Unbounded Operators
• Loss tolerant cross-Kerr enhancement via modulated squeezing