Adiabaticity in open quantum systems

Lorenzo Campos Venuti, Tameem Albash, Daniel A. Lidar, and Paolo Zanardi
Phys. Rev. A 93, 032118 – Published 14 March 2016

Abstract

We provide a rigorous generalization of the quantum adiabatic theorem for open systems described by a Markovian master equation with time-dependent Liouvillian L(t). We focus on the finite system case relevant for adiabatic quantum computing and quantum annealing. Adiabaticity is defined in terms of closeness to the instantaneous steady state. While the general result is conceptually similar to the closed-system case, there are important differences. Namely, a system initialized in the zero-eigenvalue eigenspace of L(t) will remain in this eigenspace with a deviation that is inversely proportional to the total evolution time T. In the case of a finite number of level crossings, the scaling becomes Tη with an exponent η that we relate to the rate of the gap closing. For master equations that describe relaxation to thermal equilibrium, we show that the evolution time T should be long compared to the corresponding minimum inverse gap squared of L(t). Our results are illustrated with several examples.

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  • Received 31 August 2015
  • Revised 10 February 2016

DOI:https://doi.org/10.1103/PhysRevA.93.032118

©2016 American Physical Society

Physics Subject Headings (PhySH)

General Physics

Authors & Affiliations

Lorenzo Campos Venuti1,2, Tameem Albash1,2,3, Daniel A. Lidar1,2,4,5, and Paolo Zanardi1,2

  • 1Department of Physics & Astronomy, University of Southern California, Los Angeles, California 90089, USA
  • 2Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
  • 3Information Sciences Institute, University of Southern California, Marina del Rey, California 90292, USA
  • 4Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
  • 5Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA

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Issue

Vol. 93, Iss. 3 — March 2016

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