Adiabatic theorem in the presence of noise

Michael J. O’Hara and Dianne P. O’Leary
Phys. Rev. A 77, 042319 – Published 22 April 2008

Abstract

We provide rigorous bounds for the error of the adiabatic approximation of quantum mechanics under four sources of experimental error: perturbations in the initial condition, systematic time-dependent perturbations in the Hamiltonian, coupling to low-energy quantum systems, and decoherent time-dependent perturbations in the Hamiltonian. For decoherent perturbations, we find both upper and lower bounds on the evolution time to guarantee that the adiabatic approximation performs within a prescribed tolerance. Our results include explicit definitions of constants, and we apply them to the spin-1/2 particle in a rotating magnetic field and to the superconducting flux qubit. We compare the theoretical bounds on the superconducting flux qubit to simulation results.

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  • Received 25 January 2008

DOI:https://doi.org/10.1103/PhysRevA.77.042319

©2008 American Physical Society

Authors & Affiliations

Michael J. O’Hara*

  • University of Maryland, College Park, Maryland 20742, USA

Dianne P. O’Leary

  • Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, Maryland 20742, USA and National Institute of Standards and Technology, Mathematical and Computational Sciences Division, Gaithersburg, Maryland 20899, USA

  • *mjohara@gmail.com
  • oleary@cs.umd.edu

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Issue

Vol. 77, Iss. 4 — April 2008

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