A numerical approach for calculating exact non-adiabatic terms in quantum dynamics

TL;DR

This paper introduces a new numerical method to compute the Adiabatic Gauge Potential in quantum systems, enabling better understanding of non-adiabatic effects crucial for quantum technology development.

Contribution

A novel commutator-based approach to approximate the AGP, adaptable to complex Hamiltonians and various graph structures in quantum models.

Findings

Different graph structures lead to varying scaling of AGP terms.

The method provides a tractable way to approximate non-adiabatic terms.

Application to the transverse field Ising model demonstrates versatility.

Abstract

Understanding how non-adiabatic terms affect quantum dynamics is fundamental to improving various protocols for quantum technologies. We present a novel approach to computing the Adiabatic Gauge Potential (AGP), which gives information on the non-adiabatic terms that arise from time dependence in the Hamiltonian. Our approach uses commutators of the Hamiltonian to build up an appropriate basis of the AGP, which can be easily truncated to give an approximate form when the exact result is intractable. We use this approach to study the AGP obtained for the transverse field Ising model on a variety of graphs, showing how the different underlying graph structures can give rise to very different scaling for the number of terms required in the AGP.