Trotter errors in digital adiabatic quantum simulation of quantum ℤ2 lattice gauge theory

Abstract

Trotter decomposition is the basis of the digital quantum simulation. Asymmetric and symmetric decompositions are used in our GPU demonstration of the digital adiabatic quantum simulations of (2[Formula: see text]+[Formula: see text]1)-dimensional quantum [Formula: see text] lattice gauge theory. The actual errors in Trotter decompositions are investigated as functions of the coupling parameter and the number of Trotter substeps in each step of the variation of coupling parameter. The relative error of energy is shown to be equal to the Trotter error usually defined in terms of the evolution operators. They are much smaller than the order-of-magnitude estimation. The error in the symmetric decomposition is much smaller than that in the asymmetric decomposition. The features of the Trotter errors obtained here are useful in the experimental implementation of digital quantum simulation and its numerical demonstration.