Controlling and exploring quantum systems by algebraic expression of adiabatic gauge potential

TL;DR

This paper introduces an algebraic method to determine adiabatic gauge potentials, enabling efficient control of quantum systems and detection of quantum phase transitions, with applications to spin systems and quantum annealing.

Contribution

It presents a new algebraic approach to explicitly calculate adiabatic gauge potentials and derives bounds for their performance, aiding in suppressing nonadiabatic transitions.

Findings

Explicit algebraic form of adiabatic gauge potential can be easily obtained.

Derived a lower bound for fidelity based on quantum speed limit.

Detected quantum phase transition signatures using adiabatic gauge potential.

Abstract

Adiabatic gauge potential is the origin of nonadiabatic transitions. In counterdiabatic driving, which is a method of shortcuts to adiabaticity, adiabatic gauge potential can be used to realize identical dynamics to adiabatic time evolution without requiring slow change of parameters. We introduce an algebraic expression of adiabatic gauge potential. Then, we find that the explicit form of adiabatic gauge potential can be easily determined by some algebraic calculations. We demonstrate this method by using a single-spin system, a two-spin system, and the transverse Ising chain. Moreover, we derive a lower bound for fidelity to adiabatic time evolution based on the quantum speed limit. This bound enables us to know the worst case performance of approximate adiabatic gauge potential. We can also use this bound to find dominant terms in adiabatic gauge potential to suppress nonadiabatic transitions. We apply this bound to magnetization reversal of the two-spin system and to quantum annealing of the transverse Ising chain. Adiabatic gauge potential reflects structure of energy eigenstates, and thus we also discuss detection of quantum phase transitions by using adiabatic gauge potential. We find a signature of a quantum phase transition in the transverse Ising chain.