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Advances in Mathematical Physics
Volume 2010 (2010), Article ID 169710, 20 pages
Resonant Perturbation Theory of Decoherence and Relaxation of Quantum Bits
1Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF, Canada A1C 5S7
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.
- G. Wendin and V. S. Shumeiko, “Quantum bits with Josephson junctions,” Low Temperature Physics, vol. 33, no. 9, pp. 724–744, 2007.
- D. Kinion and J. Clarke, “Microstrip superconducting quantum interference device radio-frequency amplifier: scattering parameters and input coupling,” Applied Physics Letters, vol. 92, no. 17, Article ID 172503, 3 pages, 2008.
- Y. Makhlin, G. Schön, and A. Shnirman, “Quantum-state engineering with Josephson-junction devices,” Reviews of Modern Physics, vol. 73, no. 2, pp. 357–400, 2001.
- Y. Yu, S. Han, X. Chu, S.-I. Chu, and Z. Wang, “Coherent temporal oscillations of macroscopic quantum states in a Josephson junction,” Science, vol. 296, no. 5569, pp. 889–892, 2002.
- M. H. Devoret and J. M. Martinis, “Implementing qubits with superconducting integrated circuits,” Quantum Information Processing, vol. 3, no. 1–5, pp. 163–203, 2004.
- M. Steffen, M. Ansmann, R. McDermott, et al., “State tomography of capacitively shunted phase qubits with high fidelity,” Physical Review Letters, vol. 97, no. 5, Article ID 050502, 4 pages, 2006.
- N. Katz, M. Neeley, M. Ansmann, et al., “Reversal of the weak measurement of a quantum state in a superconducting phase qubit,” Physical Review Letters, vol. 101, no. 20, Article ID 200401, 4 pages, 2008.
- A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, “Introduction to quantum noise, measurement and amplifcation,” Reviews of Modern Physics, vol. 82, pp. 1155–1208, 2010.
- M. Merkli, I. M. Sigal, and G. P. Berman, “Decoherence and thermalization,” Physical Review Letters, vol. 98, no. 13, Article ID 130401, 2007.
- M. Merkli, I. M. Sigal, and G. P. Berman, “Resonance theory of decoherence and thermalization,” Annals of Physics, vol. 323, no. 2, pp. 373–412, 2008.
- M. Merkli, G. P. Berman, and I. M. Sigal, “Dynamics of collective decoherence and thermalization,” Annals of Physics, vol. 323, no. 12, pp. 3091–3112, 2008.
- G. P. Berman, D. I. Kamenev, and V. I. Tsifrinovich, “Collective decoherence of the superpositional entangled states in the quantum Shor algorithm,” Physical Review A, vol. 71, no. 3, Article ID 032346, 5 pages, 2005.
- D. A. R. Dalvit, G. P. Berman, and M. Vishik, “Dynamics of open bosonic quantum systems in coherent state representation,” Physical Review A, vol. 73, no. 1, Article ID 013803, 2006.
- L.-M. Duan and G.-C. Guo, “Reducing decoherence in quantum-computer memory with all quantum bits coupling to the same environment,” Physical Review A, vol. 57, no. 2, pp. 737–741, 1998.
- E. Joos, H. D. Zeh, C. Kiefer, D. Giulini, J. Kupsch, and I. O. Stamatescu, Decoherence and The Appearence of a Classical World in Quantum Theory, Lecture Notes in Mathematics, Springer, Berlin, Germany, 2nd edition, 2003.
- D. Mozyrsky and V. Privman, “Adiabatic decoherence,” Journal of Statistical Physics, vol. 91, no. 3–4, pp. 787–799, 1998.
- G. M. Palma, K.-A. Suominen, and A. K. Ekert, “Quantum computers and dissipation,” Proceedings of the Royal Society A, vol. 452, no. 1946, pp. 567–584, 1996.
- J. Shao, M.-L. Ge, and H. Cheng, “Decoherence of quantum-nondemolition systems,” Physical Review E, vol. 53, no. 1, pp. 1243–1245, 1996.
- M. Merkli, G. P. Berman, F. Borgonovi, and K. Gebresellasie, “Evolution of entanglement of two qubits interacting through local and collective environments,” Quantum Physics, preprint, http://arxiv.org/abs/1001.1144.
- M. Merkli and S. Starr, “A resonance theory for open quantum systems with time-dependent dynamics,” Journal of Statistical Physics, vol. 134, pp. 871–898, 2009.
- V. Bach, M. Merkli, W. Pedra, and I. M. Sigal, “Decoherence control,” in preparation.
- H.-P Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press, Oxford, UK, 2002.
- E. B. Davies, “Markovian master equations,” Communications in Mathematical Physics, vol. 39, no. 2, pp. 91–110, 1974.
- E. B. Davies, “Markovian master equations. II,” Mathematische Annalen, vol. 219, no. 2, pp. 147–158, 1976.
- J. Dereziński and R. Früboes, Fermi Golden Rule and Open Quantum Systems, vol. 1882 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2006.
- V. Jakšić and C. A. Pillet, “From resonances to master equations,” Annales de l'Institut Henri Poincaré, vol. 67, no. 4, pp. 425–445, 1997.
- M. Merkli, “Level shift operators for open quantum systems,” Journal of Mathematical Analysis and Applications, vol. 327, no. 1, pp. 376–399, 2007.
- J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental investigation of a two-qubit decoherence-free subspace,” Physical Review Letters, vol. 92, no. 14, Article ID 147901, 4 pages, 2004.
- A. Fedorov and L. Fedichkin, “Collective decoherence of nuclear spin clusters,” Journal of Physics Condensed Matter, vol. 18, no. 12, pp. 3217–3228, 2006.
- M. Merkli, M. Mück, and I. M. Sigal, “Instability of equilibrium states for coupled heat reservoirs at different temperatures,” Journal of Functional Analysis, vol. 243, no. 1, pp. 87–120, 2007.