The first-order Trotter decomposition in the dynamical-invariant basis

TL;DR

This paper demonstrates that the first-order Trotter decomposition, when applied in the dynamical-invariant basis, has deviations of second order, offering improved accuracy for quantum Hamiltonian simulation.

Contribution

It introduces a novel application of the first-order Trotter decomposition in the dynamical-invariant basis, reducing deviation order and including a practical example related to shortcuts to adiabaticity.

Findings

Deviations are of second order in the small coefficient.

The approach applies to digital implementation of shortcuts to adiabaticity.

Provides a state-dependent inequality for deviation analysis.

Abstract

The Trotter decomposition is a basic approach to Hamiltonian simulation (digital quantum simulation). The first-order Trotter decomposition is the simplest one, whose deviations from target dynamics are of the first order of a small coefficient in terms of the infidelity. In this paper, we consider the first-order Trotter decomposition in the dynamical-invariant basis. By using a state-dependent inequality, we point out that deviations of this decomposition are of the second order of a small coefficient. Moreover, we also show that this decomposition includes a useful example, i.e., digital implementation of shortcuts to adiabaticity by counterdiabatic driving.