Integrability and chaos in the quantum brachistochrone problem

arXiv (Cornell University)

Abstract

The quantum brachistochrone problem addresses the fundamental challenge of achieving the quantum speed limit in applications aiming to realize a given unitary operation in a quantum system. Specifically, it looks into optimization of the transformation of quantum states through controlled Hamiltonians, which form a small subset in the space of the system's observables. Here we introduce a broad family of completely integrable brachistochrone protocols, which arise from a judicious choice of the control Hamiltonian subset. Furthermore, we demonstrate how the inherent stability of the completely integrable protocols makes them numerically tractable and therefore practicable as opposed to their non-integrable counterparts.

Authors 2

1. Savvas Malikis Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Instituut-Lorentz , Universiteit Leiden , Leiden , The Netherlands

2. Vadim Cheianov Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Instituut-Lorentz , Universiteit Leiden , Leiden , The Netherlands