Online ISSN:1349-8606
Progress in Informatics  
No.3 April 2006  
Page 5-18  
 
Algorithm-based analysis of collective decoherence in quantum search
Cyrus P. MASTER, Shoko UTSUNOMIYA, Yoshihisa YAMAMOTO

LINK [1] P. W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A, vol.52, p.2493, 1995.

LINK [2] A. M. Steane, “Error correcting codes in quantum theory,” Phys. Rev. Lett., vol.77, p.793, 1996.

LINK [3] A. R. Calderbank and P. W. Shor, “Good quantum error-correcting codes exist,” Phys. Rev. A, vol.54, p.1098, 1996.

LINK [4] A. M. Steane, “Multiple particle interference and quantum error correction,” Proc. R. Soc. London A, vol.452, p.2551, 1996.

LINK [5] D. Gottesman, “Class of quantum error-correcting codes saturating the quantum Hamming bound,” Phys. Rev. A, vol.54, p.1862, 1996.

LINK [6] D. Gottesman, Ph.D. thesis, Stabilizer Codes and Quantum Error Correction, California Institute of Technology, 1997.

LINK [7] E. Knill and R. Laflamme, “Power of One Bit of Quantum Information,” Phys. Rev. Lett., vol.81, p.5672, 1998.

LINK [8] J. Preskill, “Reliable quantum computers,” Proc. R. Soc. London A, vol.454, p.385, 1998.

LINK [9] P. Zanardi, “Noiseless Quantum Codes,” Phys. Rev. Lett., vol.79, p.3306, 1997.

LINK [10] P. Zanardi and M. Rasetti, “Error-avoiding codes,” Mod. Phys. Lett. B, vol.11, p.1085, 1997.

LINK [11] D. A. Lidar, I. L. Chuang, and K. B. Whaley, “Decoherence-Free Subspaces for Quantum Computation,” Phys. Rev. Lett., vol.81, p.2594, 1998.

LINK [12] P. Zanardi, “Dissipation and decoherence in a quantum register,” Phys. Rev. A, vol.57, p.3276, 1998.

LINK [13] D. A. Lidar, D. Bacon, and K. B. Whaley, “Concatenating Decoherence-Free Subspaces with Quantum Error Correcting Codes,” Phys. Rev. Lett., vol.82, p.4556, 1999.

LINK [14] D. A. Lidar and K. B. Whaley, Decoherence-Free Subspaces and Subsystems, in Irreversible Quantum Dynamics, Ed. F. Benatti and R. Floreanini, Springer-Verlag, Trieste, Italy, p.83, 2003.

LINK [15] L. Viola and S. Lloyd, “Dynamical suppresion of decoherence in two-state quantum systems,” Phys. Rev. A, vol.58, p.2733, 1998.

LINK [16] L. Viola, E. Knill, and S. Lloyd, “Dynamical Decoupling of Open Quantum Systems,” Phys. Rev. Lett., vol.82, p.2417, 1999.

LINK [17] L. Viola, S. Lloyd, and E. Knill, “Universal Control of Decoupled Quantum Systems,” Phys. Rev. Lett., vol.83, p.4888, 1999.

LINK [18] L. Viola, E. Knill, and S. Lloyd, “Dynamical Generation of Noiseless Quantum Subsystems,” Phys. Rev. Lett., vol.85, p.3520, 2000.

LINK [19] L. Viola and E. Knill, “Robust Dynamical Decoupling of Quantum Systems with Bounded Controls,” Phys. Rev. Lett., vol.90, p.037901, 2003.

LINK [20] D. Aharonov, Ph.D. thesis, Noisy Quantum Computation,The Hebrew University, 1999.

LINK [21] A. M. Turing, “On computable numbers, with an application to the Entscheidungsproblem,” Proc. London. Math. Soc., vol.2, p.230, 1936.

LINK [22] C. H. Papadimitriou, Computational Complexity, Addison-Wesley, U.S.A., 1994.

LINK [23] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information,Cambridge University Press, U.K., 2000.

LINK [24] D. Deutsch, “Quantum computational networks,” Proc. R. Soc. London A, vol.425, p.73, 1989.

LINK [25] C. H. Bennett, “Logical reversibility of computation,” IBM J. Res. Dev., vol.17, p.525, 1973.

LINK [26] E. Fredkin and T. Toffoli, “Conservative Logic,” Int. J. Theor. Phys., vol.21, p.219, 1982.

LINK [27] R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca, “Quantum Algorithms Revisited,” Proc. R. Soc. London A, vol.454, p.339, 1998.

LINK [28] M. Mosca, Ph.D. thesis, Quantum Computer Algorithms,University of Oxford, 1999.

LINK [29] P. W. Shor, “Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer,” Proc. of the 35th Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, Santa Fe, NM, pp.124-134, 1994.

LINK [30] P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM J. Comput., vol.26, p.1484, 1997.

LINK [31] L. K. Grover, “A fast quantum mechanical algorithm for database search,” in Proc. of the Twenty-Eighth Annual Symposium on the Theory of Computing, ACM Press, New York, pp.212-218, 1996.

LINK [32] L. K. Grover, “Quantum Mechanics Helps in Searching for a Needle in a Haystack,” Phys. Rev. Lett., vol.79, p.325, 1997.

LINK [33] M. Boyer, G. Brassard, P. Høyer, and A. Tapp, Tight bounds on quantum searching(1996), e-print quant-ph/9605034.

LINK [34] G. Brassard and P. Høyer, “An Exact Quantum Polynomial-Time Algorithm for Simon's Problem,” in Proc. of the Fifth Israeli Symposium on the Theory of Computing and Systems, IEEE Computer Society Press, p.12, 1997.

LINK [35] L. K. Grover, “Quantum Computers Can Search Rapidly by Using Almost Any Transformation,” Phys. Rev. Lett., vol.80, p.4329, 1998.

LINK [36] L. K. Grover, “A fast quantum mechanical algorithm for database search,” in Proc. of the Thirtieth Annual Symposium on the Theory of Computing, ACM Press, New York, pp.53-62, 1998.

LINK [37] D. F. Walls and G. J. Milburn, Quantum Optics, Springer-Verlag, Berlin, 1994.

LINK [38] Y. Yamamoto and A. Ímamoglu, Mesoscopic Quantum Optics, Wiley, New York, 1999.

LINK [39] R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev., vol.93, p.99, 1954.

LINK [40] A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A, vol.52, p.3457, 1995.

LINK [41] C. Eckart, “The application of group theory to the quantum dynamics of monatomic systems,” Rev. Mod. Phys., vol.2, p.305, 1930.

LINK [42] E. P. Wigner, Gruppentheorie, Vieweg, 1931.

LINK [43] J. J. Sakurai, Modern Quantum Mechanics, Addison-Wesley, U.S.A., 1994.

LINK [44] C. P. Master, Ph.D. thesis, Quantum Computing Under Real-World Constraints:Efficiency of an Ensemble Quantum Algorithm and Fighting Decoherence by Gate Design, Stanford University, 2005.