Error reduction in quantum annealing using boundary cancellation: Only the end matters

Lorenzo Campos Venuti and Daniel A. Lidar
Phys. Rev. A 98, 022315 – Published 13 August 2018

Abstract

The adiabatic theorem of quantum mechanics states that the error between an instantaneous eigenstate of a time-dependent Hamiltonian and the state given by quantum evolution of duration τ is upper bounded by C/τ for some positive constant C. It has been known for decades that this error can be reduced to Ck/τk+1 if the Hamiltonian has vanishing derivatives up to order k at the beginning and end of the evolution. Here we extend this result to open systems described by a time-dependent Liouvillian superoperator. We find that the same results holds provided the Liouvillian has vanishing derivatives up to order k only at the end of the evolution. This asymmetry is ascribable to the arrow of time inherent in open system evolution. We further investigate whether it is possible to satisfy the required assumptions by controlling only the system, as required for realistic implementations. Surprisingly, we find the answer to be affirmative. We establish this rigorously in the setting of the Davies-Lindblad adiabatic master equation, and numerically in the setting of two different time-dependent Redfield-type master equations we derive. The results are shown to be stable with respect to imperfections in the preparation. Finally, we prove that the results hold also in a fully Hamiltonian model.

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  • Received 20 June 2018

DOI:https://doi.org/10.1103/PhysRevA.98.022315

©2018 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Lorenzo Campos Venuti1,2 and Daniel A. Lidar1,2,3,4

  • 1Department of Physics and 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
  • 3Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
  • 4Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA

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Issue

Vol. 98, Iss. 2 — August 2018

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