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Advances in Mathematical Physics
Volume 2010 (2010), Article ID 169710, 20 pages
doi:10.1155/2010/169710
Review Article

Resonant Perturbation Theory of Decoherence and Relaxation of Quantum Bits

M. Merkli,1 G. P. Berman,2 and I. M. Sigal3

1Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF, A1C 5S7, Canada
2Theoretical Division, MS B213, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
3Department of Mathematics, University of Toronto, Toronto, ON, M5S2E4, Canada

Received 31 August 2009; Accepted 10 February 2010

Academic Editor: Shao-Ming Fei

Copyright © 2010 M. Merkli et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We describe our recent results on the resonant perturbation theory of decoherence and relaxation for quantum systems with many qubits. The approach represents a rigorous analysis of the phenomenon of decoherence and relaxation for general N-level systems coupled to reservoirs of bosonic fields. We derive a representation of the reduced dynamics valid for all times 𝑡 ≥ 0 and for small but fixed interaction strength. Our approach does not involve master equation approximations and applies to a wide variety of systems which are not explicitly solvable.