Method for constructing shortcuts to adiabaticity by a substitute of counterdiabatic driving terms

TL;DR

This paper introduces a practical method to create shortcuts to adiabaticity by designing substitute Hamiltonians that avoid complex counterdiabatic terms, enabling faster quantum processes in both Hermitian and non-Hermitian systems.

Contribution

The paper presents a novel approach to construct shortcuts to adiabaticity using substitute Hamiltonians that simplify implementation and speed up quantum adiabatic processes.

Findings

Applicable to Hermitian and non-Hermitian systems

Successfully applied to Landau-Zener model

Provides multiple design options for practical Hamiltonians

Abstract

We propose an efficientmethod to construct shortcuts to adiabaticity through designing a substitute Hamiltonian to try to avoid the defect in which the speed-up protocol' Hamiltonian may involve terms which are difficult to realize in practice. We show that as long as the counterdiabatic coupling terms-even only some of them-have been nullified by the additional Hamiltonian, the corresponding shortcuts to the adiabatic process could be constructed and the adiabatic process would be sped up. As an application example, we apply this method to the popular Landau-Zener model for the realization of fast population inversion. The results show that in both Hermitian and non-Hermitian systems, we can design different additional Hamiltonians to replace the traditional counterdiabatic driving Hamiltonian to speed up the process. This method provides many choices for designing additional terms of the Hamiltonian such that one can choose a realizable model in practice.