Unitary deformations of counterdiabatic driving

TL;DR

This paper introduces a systematic method for deforming counterdiabatic Hamiltonians using unitary transformations, enabling improved adiabatic control of quantum states with explicit examples and theoretical insights.

Contribution

It presents a novel approach to deform counterdiabatic driving Hamiltonians via unitary transformations, supported by explicit examples and a connection to the quantum brachistochrone equation.

Findings

Explicit forms of deformed Hamiltonians for specific systems

Existence of a nontrivial dynamical invariant in the deformed system

The method provides a systematic way to control quantum states adiabatically

Abstract

We study a deformation of the counterdiabatic-driving Hamiltonian as a systematic strategy for an adiabatic control of quantum states. Using a unitary transformation, we design a convenient form of the driver Hamiltonian. We apply the method to a particle in a confining potential and discrete systems to find explicit forms of the Hamiltonian and discuss the general properties. The method is derived by using the quantum brachistochrone equation, which shows the existence of a nontrivial dynamical invariant in the deformed system.