Quantum adiabatic brachistochrone for open systems

TL;DR

This paper introduces a variational approach to determine the quantum adiabatic brachistochrone for open quantum systems, optimizing the evolution time based on energy gaps and adiabatic speed, with applications to various quantum processes.

Contribution

It develops a novel variational principle and numerical protocol for computing the quantum adiabatic brachistochrone in open systems, extending previous methods to non-unitary dynamics.

Findings

Successfully applied to STIRAP, Deutsch-Jozsa, and transmon qutrit systems.

Established conditions for equivalence between open and closed system QABs.

Provided a numerical protocol for arbitrary quantum systems with feasible simulations.

Abstract

We propose a variational principle to compute a quantum adiabatic brachistochrone (QAB) for open systems. Using the notion of "adiabatic speed" based on the energy gaps, we derive a Lagrangian associated to the functional measuring the time spent to achieve adiabatic behavior, which in turn allows us to perform the optimization. The QAB is illustrated for non-unitary dynamics of STIRAP process, the Deutsch-Jozsa quantum computing algorithm and of a transmon qutrit. A numerical protocol is devised, which allows to compute the QAB for arbitrary quantum systems for which exact simulations can be afforded. We also establish sufficient conditions for the equivalence between the Lagrangians, and thus the QAB, of open and closed systems.