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Advances in Mathematical Physics
Volume 2010 (2010), Article ID 365653, 10 pages
Quantum Computing in Decoherence-Free Subspace Constructed by Triangulation
1Department of Physics, School of Science, Wuhan University of Technology, Wuhan 430070, China
2Centre for Advanced Nanotechnology, University of Toronto, Toronto, Canada M5S 3E4
Received 17 August 2009; Revised 2 November 2009; Accepted 30 December 2009
Academic Editor: Nai-Huan Jing
Copyright © 2010 Qiao Bi 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.
- D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I.-O. Stamatescu, and H. D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory, Springer, Berlin, Germany, 1996.
- P. Zanardi and M. Rasetti, “Error avoiding quantum codes,” Modern Physics Letters B, vol. 11, no. 25, pp. 1085–1093, 1997.
- P. Zanardi and M. Rasetti, “Noiseless quantum codes,” Physical Review Letters, vol. 79, no. 17, pp. 3306–3309, 1997.
- P. Zanardi, “Virtual quantum subsystems,” Physical Review Letters, vol. 87, no. 7, Article ID 077901, 4 pages, 2001.
- A. Barenco, A. Berthiaume, D. Deutsch, A. Ekert, R. Jozsa, and C. Macchiavello, “Stabilization of quantum computations by symmetrization,” SIAM Journal on Computing, vol. 26, no. 5, pp. 1541–1557, 1997.
- L.-M. Duan and G.-C. Guo, “Preserving coherence in quantum computation by pairing quantum bits,” Physical Review Letters, vol. 79, no. 10, pp. 1953–1956, 1997.
- D. A. Lidar, I. L. Chuang, and K. B. Whaley, “Decoherence-free subspaces for quantum computation,” Physical Review Letters, vol. 81, no. 12, pp. 2594–2597, 1998.
- D. A. Lidar, D. Bacon, and K. B. Whaley, “Concatenating decoherence-free subspaces with quantum error correcting codes,” Physical Review Letters, vol. 82, no. 22, pp. 4556–4559, 1999.
- D. Bacon, J. Kempe, D. A. Lidar, and K. B. Whaley, “Universal fault-tolerant quantum computation on decoherence-free subspaces,” Physical Review Letters, vol. 85, no. 8, pp. 1758–1761, 2000.
- A. Shabani and D. A. Lidar, “Theory of initialization-free decoherence-free subspaces and subsystems,” Physical Review A, vol. 72, no. 4, Article ID 042303, 14 pages, 2005.
- G. Gordon, G. Kurizki, and D. A. Lidar, “Optimal dynamical decoherence control of a qubit,” Physical Review Letters, vol. 101, no. 1, Article ID 010403, 4 pages, 2008.
- D. A. Lidar, “Towards fault tolerant adiabatic quantum computation,” Physical Review Letters, vol. 100, no. 16, Article ID 160506, 4 pages, 2008.
- S. D. Kunikeev and D. A. Lidar, “Spin density matrix of a two-electron system. II. Application to a system of two quantum dots,” Physical Review B, vol. 77, no. 4, Article ID 045320, 19 pages, 2008.
- A. Shabani and D. A. Lidar, “Maps for general open quantum systems and a theory of linear quantum error correction,” Physical Review A, vol. 80, no. 1, Article ID 012309, 11 pages, 2009.
- O. Oreshkov, T. A. Brun, and D. A. Lidar, “Fault-tolerant holonomic quantum computation,” Physical Review Letters, vol. 102, no. 7, Article ID 070502, 4 pages, 2009.
- S. De Filippo, “Quantum computation using decoherence-free states of the physical operator algebra,” Physical Review A, vol. 62, no. 5, Article ID 052307, 6 pages, 2000.
- C. Schön and A. Beige, “Analysis of a two-atom double-slit experiment based on environment-induced measurements,” Physical Review A, vol. 64, no. 2, Article ID 023806, 9 pages, 2001.
- L. Viola, “Quantum control via encoded dynamical decoupling,” Physical Review A, vol. 66, no. 1, Article ID 012307, 10 pages, 2002.
- S. Gheorghiu-Svirschevski, “From Davydov solitons to decoherence-free subspaces: self-consistent propagation of coherent-product states,” Physical Review E, vol. 64, no. 5, Article ID 051907, 17 pages, 2001.
- P. Facchi and S. Pascazio, “Quantum Zeno subspaces and dynamical superselection rules,” in The Physics of Communication: Proceedings of the XXII Solvay Conference on Physics, pp. 251–286, Delphi Lamia, Greece, November 2001.
- B. Qiao, H. E. Ruda, and M. S. Zhan, “Two-qubit quantum computing in a projected subspace,” Physical Review A, vol. 65, no. 4, Article ID 042325, 11 pages, 2002.
- M. S. Tame, M. Paternostro, and M. S. Kim, “One-way quantum computing in a decoherence-free subspace,” New Journal of Physics, vol. 9, Article ID 201, 2007.
- C. Bény, A. Kempf, and D. W. Kribs, “Generalization of quantum error correction via the Heisenberg picture,” Physical Review Letters, vol. 98, no. 10, Article ID 100502, 4 pages, 2007.
- D. A. Lidar and K. B. Whaley, “Decoherence-free subspaces and subsystems,” in Irreversible Quantum Dynamics, F. Benatti and R. Floreanini, Eds., vol. 622 of Lecture Notes in Physics, pp. 83–120, Springer, Berlin, Germany, 2003.
- D. Kribs, R. Laflamme, and D. Poulin, “Unified and generalized approach to quantum error correction,” Physical Review Letters, vol. 94, no. 18, Article ID 180501, 4 pages, 2005.
- D. W. Kribs, R. Laflamme, D. Poulin, and M. Lesosky, “Operator quantum error correction,” Quantum Information and Computation, vol. 6, no. 4-5, pp. 382–399, 2006.
- C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Physical Review A, vol. 54, no. 5, pp. 3824–3851, 1996.
- E. Knill and R. Laflamme, “Theory of quantum error-correcting codes,” Physical Review A, vol. 55, no. 2, pp. 900–911, 1997.
- M.-D. Choi and D. W. Kribs, “Method to find quantum noiseless subsystems,” Physical Review Letters, vol. 96, no. 5, Article ID 050501, 4 pages, 2006.
- E. Knill, “Protected realizations of quantum information,” Physical Review A, vol. 74, no. 4, Article ID 042301, 11 pages, 2006.
- P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, “Experimental verification of decoherence-free subspaces,” Science, vol. 290, no. 5491, pp. 498–501, 2000.
- Q. Zhang, J. Yin, T.-Y. Chen, et al., “Experimental fault-tolerant quantum cryptography in a decoherence-free subspace,” Physical Review A, vol. 73, no. 2, Article ID 020301, 4 pages, 2006.
- M. Mohseni, J. S. Lundeen, K. J. Resch, and A. M. Steinberg, “Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm,” Physical Review Letters, vol. 91, no. 18, Article ID 187903, 4 pages, 2003.
- 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, 2004.
- I. Antoniou and S. Tasaki, “Generalized spectral decompositions of mixing dynamical systems,” International Journal of Quantum Chemistry, vol. 46, pp. 425–474, 1993.
- T. Petrosky and I. Prigogine, “Alternative formulation of classical and quantum dynamics for non-integrable systems,” Physica A, vol. 175, no. 1, pp. 146–209, 1991.
- B. Qiao, Subdynamics Theory and Application in Complex Dynamical System, Wuhan University of Technology Press, Wuhan, China, 1998.
- A. Bohm, H. D. Doebner, and P. Kielanowski, Irreversibility and Causality, Semigroups and Rigged Hilbert Spaces, Springer, Berlin, Germany, 1998.
- A. Bohm and M. Gadella, Dirac Kets, Gamow Vector and Gel'fand Triplets, Springer, Berlin, Germany, 1989.
- B. Qiao and H. E. Ruda, “Quantum computing using entanglement states in a photonic band gap,” Journal of Applied Physics, vol. 86, no. 9, pp. 5237–5244, 1999.
- R. Balescu, Equilibrium and Non-Equilibrium Statistical Mechanics, John Wiley & Sons, New York, NY, USA, 1975.
- B. E. Kane, “A silicon-based nuclear spin quantum computer,” Nature, vol. 393, no. 6681, pp. 133–137, 1998.
- R. Vrijen, E. Yablonovitch, K. Wang, et al., “Electron-spin-resonance transistors for quantum computing in silicon-germanium heterostructures,” Physical Review A, vol. 62, no. 1, Article ID 012306, 10 pages, 2000.
- D. Loss and D. P. Divincenzo, “Quantum computation with quantum dots,” Physical Review A, vol. 57, no. 1, pp. 120–126, 1998.
- W. A. Coish and D. Loss, “Quantum computing with spins in solids,” http://arxiv.org/abs/cond-mat/0606550.