Generalized transitionless quantum driving for open quantum systems

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.

17 pages (including Appendix) and 4 figures

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• Lewis-Riesenfeld invariants and transitionless tracking algorithm
• Adiabatic approximation in open quantum systems
• Universal Work Fluctuations during Shortcuts To Adiabaticity by Counterdiabatic Driving
• Decoherence in adiabatic quantum computation
• Reverse engineering of a Hamiltonian by designing the evolution operators
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Cited by in corpus (11)

• Shortcuts to adiabaticity: theoretical framework, relations between different methods, and versatile approximations
• Robustness of controlled Hamiltonian approaches to unitary quantum gates
• Failure of the geometric approach prediction of excess work scaling for open and isolated quantum systems
• Quantum annealing sampling with a bias field
• Dynamics of a driven open double two-level system and its entanglement generation
• Improving Variational Counterdiabatic Driving with Weighted Actions and Computer Algebra
• Quantum Transport Protected by Acceleration From Nonadiabaticity and Dissipation
• Speeding up Lindblad dynamics via time-rescaling engineering
• Counterdiabatic driving for random-gap Landau-Zener transitions
• Unconventional mechanism of virtual-state population through dissipation
• Environment-Assisted Shortcuts to Adiabaticity