Trotter error with commutator scaling for the Fermi-Hubbard model

Abstract

We derive higher-order error bounds with small prefactors for a general Trotter product formula, generalizing a result of Childs et al. [Phys. Rev. X 11, 011020 (2021)]. We then apply these bounds to the real-time quantum time evolution operator governed by the Fermi-Hubbard Hamiltonian on one-dimensional and two-dimensional square and triangular lattices. The main technical contribution of our work is a symbolic evaluation of nested commutators between hopping and interaction terms for a given lattice geometry. The calculations result in explicit expressions for the error bounds in terms of the time step and Hamiltonian coefficients. Comparison with the actual Trotter error (evaluated on a small system) indicates that the bounds still overestimate the error.

12 pages, 4 figures

References in corpus (2)

• Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation
• Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure

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