Generalized transitionless quantum driving for open quantum systems

TL;DR

This paper introduces a generalized method for transitionless quantum driving in open quantum systems, enabling shortcuts to adiabaticity by deriving a generalized Lindbladian that accounts for phase freedom and can be engineered for specific quantum algorithms.

Contribution

It develops a unified framework for transitionless quantum driving in open systems, extending previous approaches and allowing for the engineering of time-independent master equations.

Findings

Derived the generalized transitionless Lindbladian for open systems.

Showed how to engineer time-independent master equations matching standard driving.

Applied the method to quantum algorithms like Deutsch and Landau-Zener models.

Abstract

A general approach for transitionless quantum driving in open quantum systems is introduced. Under the assumption of adiabatic evolution for time-local master equations, we derive the generalized transitionless Lindbladian required to implement a shortcut to adiabaticity in an open system scenario. The general counter-diabatic Lindbladian obtained accounts for a phase freedom, which translates into a set of free parameters throughout the dynamics. We then discuss how our generalized approach allows us to recover the transitionless Lindbladian introduced by G. Vacanti et al. [New J. Phys. 16, 053017 (2014)]. We then show how to engineer time-independent master equations that provide the same dynamics as the time-dependent master equation provided by the standard transitionless quantum driving in open systems. We illustrate our results by applying them both to the adiabatic Deutsch algorithm under dephasing and to the Landau-Zener Hamiltonian under bit-phase-flip.