Trotter error with commutator scaling for the Fermi-Hubbard model
- URL: http://arxiv.org/abs/2306.10603v2
- Date: Tue, 26 Sep 2023 21:25:49 GMT
- Title: Trotter error with commutator scaling for the Fermi-Hubbard model
- Authors: Ansgar Schubert and Christian B. Mendl
- Abstract summary: We derive higher-order error bounds with small prefactors for a general Trotter product formula.
We then apply these bounds to the real-time quantum time evolution operator governed by the Fermi-Hubbard Hamiltonian.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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