메뉴 건너뛰기




Volumn 17, Issue 6, 2007, Pages 1169-1220

Decoherence in quantum walks - A review

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ERROR CORRECTION; PROBLEM SOLVING; RANDOM PROCESSES;

EID: 40649112201     PISSN: 09601295     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0960129507006354     Document Type: Article
Times cited : (364)

References (106)
  • 1
    • 17644370731 scopus 로고    scopus 로고
    • A note on graphs resistant to quantum uniform mixing
    • ArXiv: quant-ph/0308073
    • Adamczak, W., Andrew, K., Hernberg, P. and Tamon, C. (2003) A note on graphs resistant to quantum uniform mixing. ArXiv: quant-ph/0308073.
    • (2003)
    • Adamczak, W.1    Andrew, K.2    Hernberg, P.3    Tamon, C.4
  • 2
    • 38049002002 scopus 로고    scopus 로고
    • Adamczak, W., Andrew, K., Bergen, L., Ethier, D., Hernberg, P., Lin, J. and Tamon, C. (2007) Non-uniform mixing of quantum walk on cycles. Intl. J. Quantum Inf. (to appear). See also ArXiv: 0708.2096.
    • Adamczak, W., Andrew, K., Bergen, L., Ethier, D., Hernberg, P., Lin, J. and Tamon, C. (2007) Non-uniform mixing of quantum walk on cycles. Intl. J. Quantum Inf. (to appear). See also ArXiv: 0708.2096.
  • 5
    • 0344120640 scopus 로고    scopus 로고
    • On mixing in continuous-time quantum walks on some circulant graphs
    • Ahmadi, A., Belk, R., Tamon, C. and Wendler, C. (2003) On mixing in continuous-time quantum walks on some circulant graphs. Quantum Information and Computation 3 (6) 611-618.
    • (2003) Quantum Information and Computation , vol.3 , Issue.6 , pp. 611-618
    • Ahmadi, A.1    Belk, R.2    Tamon, C.3    Wendler, C.4
  • 6
    • 28844487425 scopus 로고    scopus 로고
    • Alagić, G. and Russell, A. (2005) Decoherence in quantum walks on the hypercube. Phys. Rev. A 72 0062304.
    • Alagić, G. and Russell, A. (2005) Decoherence in quantum walks on the hypercube. Phys. Rev. A 72 0062304.
  • 7
    • 5444262221 scopus 로고    scopus 로고
    • Quantum walks and their algorithmic applications
    • Ambainis, A. (2003) Quantum walks and their algorithmic applications. Intl. J. Quantum Information 1 (4) 507-518.
    • (2003) Intl. J. Quantum Information , vol.1 , Issue.4 , pp. 507-518
    • Ambainis, A.1
  • 10
    • 24244444170 scopus 로고
    • Absence of diffusion in certain random lattices
    • Anderson, P. W. (1958) Absence of diffusion in certain random lattices. Phys. Rev. 109 (5) 1492-1505.
    • (1958) Phys. Rev , vol.109 , Issue.5 , pp. 1492-1505
    • Anderson, P.W.1
  • 15
    • 0038514040 scopus 로고    scopus 로고
    • Quantum random walks with decoherent coins
    • Brun, T. A., Carteret, H.A. and Ambainis, A. (2003a) Quantum random walks with decoherent coins. Phys. Rev. A 67 032304.
    • (2003) Phys. Rev. A , vol.67 , pp. 032304
    • Brun, T.A.1    Carteret, H.A.2    Ambainis, A.3
  • 16
    • 0242321669 scopus 로고    scopus 로고
    • The quantum to classical transition for random walks
    • Brun, T. A., Carteret, H. A. and Ambainis, A. (2003b) The quantum to classical transition for random walks. Phys. Rev. Lett. 91 (13) 130602.
    • (2003) Phys. Rev. Lett , vol.91 , Issue.13 , pp. 130602
    • Brun, T.A.1    Carteret, H.A.2    Ambainis, A.3
  • 18
    • 43649099587 scopus 로고    scopus 로고
    • Universal mixing of quantum walk on graphs
    • ArXiv: quant-ph/0608044
    • Carlson, W., Ford, A., Harris, E., Rosen, J., Tamon, C. and Wrobel, K. (2006) Universal mixing of quantum walk on graphs. ArXiv: quant-ph/0608044.
    • (2006)
    • Carlson, W.1    Ford, A.2    Harris, E.3    Rosen, J.4    Tamon, C.5    Wrobel, K.6
  • 20
    • 0242298101 scopus 로고    scopus 로고
    • Three routes to the exact asymptotics for the one-dimensional quantum walk
    • Carteret, H.A., Ismail, M. A. and Richmond, B. (2003) Three routes to the exact asymptotics for the one-dimensional quantum walk. J. Phys. A 36 (33) 8775-8795.
    • (2003) J. Phys. A , vol.36 , Issue.33 , pp. 8775-8795
    • Carteret, H.A.1    Ismail, M.A.2    Richmond, B.3
  • 22
    • 19544365900 scopus 로고    scopus 로고
    • Spatial search by quantum walk
    • Childs, A. and Goldstone, J. (2004a) Spatial search by quantum walk. Phys. Rev. A 70 022314.
    • (2004) Phys. Rev. A , vol.70 , pp. 022314
    • Childs, A.1    Goldstone, J.2
  • 23
    • 19744381153 scopus 로고    scopus 로고
    • Spatial search and the Dirac equation
    • Childs, A.M. and Goldstone, J. (2004b) Spatial search and the Dirac equation. Phys. Rev. A 70 042312.
    • (2004) Phys. Rev. A , vol.70 , pp. 042312
    • Childs, A.M.1    Goldstone, J.2
  • 26
    • 0025720957 scopus 로고
    • A random polynomial-time algorithm for approximating the volume of convex bodies
    • Dyer, M., Frieze, A. and Kannan, R. (1991) A random polynomial-time algorithm for approximating the volume of convex bodies. J. of the ACM 38 (1) 1-17.
    • (1991) J. of the ACM , vol.38 , Issue.1 , pp. 1-17
    • Dyer, M.1    Frieze, A.2    Kannan, R.3
  • 27
    • 33144467079 scopus 로고    scopus 로고
    • Decoherence induced by a chaotic environment: A quantum walker with a complex coin
    • Ermann, L., Paz, J.P. and Sraceno, M. (2006) Decoherence induced by a chaotic environment: a quantum walker with a complex coin. Phys. Rev. A 73 (1) 012302.
    • (2006) Phys. Rev. A , vol.73 , Issue.1 , pp. 012302
    • Ermann, L.1    Paz, J.P.2    Sraceno, M.3
  • 28
    • 4243657256 scopus 로고    scopus 로고
    • Quantum computation and decison trees
    • Farhi, E. and Gutmann, S. (1998) Quantum computation and decison trees. Phys. Rev. A 58 915-928.
    • (1998) Phys. Rev. A , vol.58 , pp. 915-928
    • Farhi, E.1    Gutmann, S.2
  • 29
    • 33645791929 scopus 로고    scopus 로고
    • Mixing and decoherence in continuous time quantum walks on cycles
    • Fedichkin, L., Solenov, D. and Tamon, C. (2006) Mixing and decoherence in continuous time quantum walks on cycles. Quantum Information and Computation 6 (3) 263-276.
    • (2006) Quantum Information and Computation , vol.6 , Issue.3 , pp. 263-276
    • Fedichkin, L.1    Solenov, D.2    Tamon, C.3
  • 30
    • 1842455709 scopus 로고    scopus 로고
    • Scattering theory and discrete-time quantum walks
    • Feldman, E. and Hillery, M. (2004) Scattering theory and discrete-time quantum walks. Phys. Lett. A 324 (3) 277.
    • (2004) Phys. Lett. A , vol.324 , Issue.3 , pp. 277
    • Feldman, E.1    Hillery, M.2
  • 31
    • 5344230456 scopus 로고
    • Quantum mechanical computers
    • Feynman, R. P. (1986) Quantum mechanical computers. Found. Phys. 16 507.
    • (1986) Found. Phys , vol.16 , pp. 507
    • Feynman, R.P.1
  • 33
    • 3543009603 scopus 로고    scopus 로고
    • Quantum random walks with history dependence
    • Flitney, A. P., Abott, D. and Johnson, N. F (2004) Quantum random walks with history dependence. J. Phys. A 37 7581-7591.
    • (2004) J. Phys. A , vol.37 , pp. 7581-7591
    • Flitney, A.P.1    Abott, D.2    Johnson, N.F.3
  • 34
    • 28844492557 scopus 로고    scopus 로고
    • Two examples of discrete-time quantum walks taking continuous steps
    • Gottlieb, A. D. (2004) Two examples of discrete-time quantum walks taking continuous steps. Phys. Rev. E 72 (4) 047102.
    • (2004) Phys. Rev. E , vol.72 , Issue.4 , pp. 047102
    • Gottlieb, A.D.1
  • 36
    • 42749101866 scopus 로고    scopus 로고
    • Weak limits for quantum random walks
    • Grimmett, G., Janson, S. and Scudo, P. (2004) Weak limits for quantum random walks. Phys. Rev. E69 026119.
    • (2004) Phys. Rev. E , vol.69 , pp. 026119
    • Grimmett, G.1    Janson, S.2    Scudo, P.3
  • 38
    • 0029701737 scopus 로고    scopus 로고
    • A fast quantum mechanical algorithm for database search
    • ACM
    • Grover, L. K. (1996) A fast quantum mechanical algorithm for database search. In: Proc. 28th Annual ACM STOC., ACM 212.
    • (1996) Proc. 28th Annual ACM STOC , pp. 212
    • Grover, L.K.1
  • 40
    • 0000900066 scopus 로고    scopus 로고
    • Measurements with a noninvasive detector and dephasing mechanism
    • Gurvitz, S. A. (1997) Measurements with a noninvasive detector and dephasing mechanism. Phys. Rev. B 56 15215.
    • (1997) Phys. Rev. B , vol.56 , pp. 15215
    • Gurvitz, S.A.1
  • 42
    • 18144439004 scopus 로고    scopus 로고
    • Localization of two-dimensional quantum walks
    • Inui, N., Konishi, Y. and Konno, N. (2004) Localization of two-dimensional quantum walks. Phys. Rev. A 69 052323.
    • (2004) Phys. Rev. A , vol.69 , pp. 052323
    • Inui, N.1    Konishi, Y.2    Konno, N.3
  • 43
    • 0034832758 scopus 로고    scopus 로고
    • A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries
    • ACM
    • Jerrum, M., Sinclair, A. and Vigoda, E. (2001) A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries. In: Proc. 33rd Annual ACM STOC., ACM 712-721.
    • (2001) Proc. 33rd Annual ACM STOC , pp. 712-721
    • Jerrum, M.1    Sinclair, A.2    Vigoda, E.3
  • 44
    • 33845650883 scopus 로고    scopus 로고
    • Localization and its consequences for quantum walk algorithms and quantum communication
    • ArXiv: quant-ph/0606205
    • Keating, J. P., Linden, N., Matthews, J. C. F. and Winter, A. (2006) Localization and its consequences for quantum walk algorithms and quantum communication. ArXiv: quant-ph/0606205.
    • (2006)
    • Keating, J.P.1    Linden, N.2    Matthews, J.C.F.3    Winter, A.4
  • 45
    • 10244250337 scopus 로고    scopus 로고
    • Quantum random walk algorithms
    • Kempe, J. (2003a) Quantum random walk algorithms. Contemp. Phys. 44 (3) 302-327.
    • (2003) Contemp. Phys , vol.44 , Issue.3 , pp. 302-327
    • Kempe, J.1
  • 46
    • 35248893912 scopus 로고    scopus 로고
    • Quantum random walks hit exponentially faster
    • Proc. 7th Intl. Workshop on Randomization and Approximation Techniques in Computer Science RANDOM '03
    • Kempe, J. (2003b) Quantum random walks hit exponentially faster. In: Proc. 7th Intl. Workshop on Randomization and Approximation Techniques in Computer Science (RANDOM '03). Springer-Verlag Lecture Notes in Computer Science 354-369.
    • (2003) Springer-Verlag Lecture Notes in Computer Science , vol.354-369
    • Kempe, J.1
  • 47
    • 24644478594 scopus 로고    scopus 로고
    • Quantum random walks hit exponentially faster
    • Kempe, J. (2005) Quantum random walks hit exponentially faster. Probability Th. and Related Fields 133 (2) 215-235.
    • (2005) Probability Th. and Related Fields , vol.133 , Issue.2 , pp. 215-235
    • Kempe, J.1
  • 48
    • 33845540663 scopus 로고    scopus 로고
    • Kendon, V. (2006a) Quantum walks on general graphs. Int. J. Quantum Inf. 4 (5) 791-805. See also ArXiv: quant-ph/0306140.
    • Kendon, V. (2006a) Quantum walks on general graphs. Int. J. Quantum Inf. 4 (5) 791-805. See also ArXiv: quant-ph/0306140.
  • 49
    • 33845616399 scopus 로고    scopus 로고
    • A random walk approach to quantum algorithms
    • Kendon, V. (2006b) A random walk approach to quantum algorithms. Phil. Trans. Roy. Soc. A 364 3407-3422.
    • (2006) Phil. Trans. Roy. Soc. A , vol.364 , pp. 3407-3422
    • Kendon, V.1
  • 50
    • 43649103474 scopus 로고    scopus 로고
    • Optimal computation with non-unitary quantum walks. ArXiv: Quant-ph/0610240. To appear in Theor. Comp. Sci
    • Kendon, V. and Maloyer, O. (2006) Optimal computation with non-unitary quantum walks. ArXiv: quant-ph/0610240. To appear in Theor. Comp. Sci. A (2008) as a postproceedings volume for CiE 2006.
    • (2006) A (2008) as a postproceedings volume for CiE
    • Kendon, V.1    Maloyer, O.2
  • 52
    • 10844250753 scopus 로고    scopus 로고
    • Decoherence can be useful in quantum walks
    • Kendon, V. and Tregenna, B. (2003) Decoherence can be useful in quantum walks. Phys. Rev. A 67 042315.
    • (2003) Phys. Rev. A , vol.67 , pp. 042315
    • Kendon, V.1    Tregenna, B.2
  • 53
    • 33344466908 scopus 로고    scopus 로고
    • Complementarity and quantum walks
    • Kendon, V.M. and Sanders, B.C. (2004) Complementarity and quantum walks. Phys. Rev. A 71 022307.
    • (2004) Phys. Rev. A , vol.71 , pp. 022307
    • Kendon, V.M.1    Sanders, B.C.2
  • 54
    • 0142057225 scopus 로고    scopus 로고
    • Quantum walk on the line as an interference phenomenon
    • Knight, P. L., Roldán, E. and Sipe, J. E. (2003) Quantum walk on the line as an interference phenomenon. Phys. Rev. A 68 020301(R).
    • (2003) Phys. Rev. A , vol.68
    • Knight, P.L.1    Roldán, E.2    Sipe, J.E.3
  • 55
    • 3142751330 scopus 로고    scopus 로고
    • Propagating quantum walks: The origin of interference structures
    • Knight, P. L., Roldán, E. and Sipe, J. E. (2004) Propagating quantum walks: the origin of interference structures. J. Mod. Opt. 51 1761-1777.
    • (2004) J. Mod. Opt , vol.51 , pp. 1761-1777
    • Knight, P.L.1    Roldán, E.2    Sipe, J.E.3
  • 56
    • 2342589973 scopus 로고    scopus 로고
    • Quantum random walks in one dimension
    • Konno, N. (2002) Quantum random walks in one dimension. Quantum Information Processing 1 (5) 345-354.
    • (2002) Quantum Information Processing , vol.1 , Issue.5 , pp. 345-354
    • Konno, N.1
  • 57
    • 28844485932 scopus 로고    scopus 로고
    • A new type of limit theorems for the one-dimensional quantum random walk
    • Konno, N. (2005a) A new type of limit theorems for the one-dimensional quantum random walk. Journal of the Mathematical Society of Japan 57 (4) 1179-1195.
    • (2005) Journal of the Mathematical Society of Japan , vol.57 , Issue.4 , pp. 1179-1195
    • Konno, N.1
  • 58
    • 29144473642 scopus 로고    scopus 로고
    • A path integral approach for disordered quantum walks in one dimension
    • Konno, N. (2005b) A path integral approach for disordered quantum walks in one dimension. Fluctuation and Noise Letters 5 (4) 529-537.
    • (2005) Fluctuation and Noise Letters , vol.5 , Issue.4 , pp. 529-537
    • Konno, N.1
  • 59
    • 43649091846 scopus 로고    scopus 로고
    • Konno, N., Namiki, T. and Soshi, T. (2004) Symmetricity of distribution for the one-dimentional Hadamard walk. Interdisciplinary Infor. Sci. 10 (1) 11-22.
    • Konno, N., Namiki, T. and Soshi, T. (2004) Symmetricity of distribution for the one-dimentional Hadamard walk. Interdisciplinary Infor. Sci. 10 (1) 11-22.
  • 60
    • 0001257553 scopus 로고    scopus 로고
    • Quantum chaos on graphs
    • Kottos, T. and Smilansky, U. (1997) Quantum chaos on graphs. Phys. Rev. Lett. 79 4794-4797.
    • (1997) Phys. Rev. Lett , vol.79 , pp. 4794-4797
    • Kottos, T.1    Smilansky, U.2
  • 61
    • 33747055081 scopus 로고    scopus 로고
    • Quantum walks with random phase shifts
    • Košík, J., Bužek, V. and Hillery, M. (2006) Quantum walks with random phase shifts. Phys. Rev. A 74 (2) 022310.
    • (2006) Phys. Rev. A , vol.74 , Issue.2 , pp. 022310
    • Košík, J.1    Bužek, V.2    Hillery, M.3
  • 62
    • 27144544067 scopus 로고    scopus 로고
    • Lower and upper bounds on the secret key rate for QKD protocols using one-way classical communication
    • Kraus, B., Gisin, N. and Renner, R. (2005) Lower and upper bounds on the secret key rate for QKD protocols using one-way classical communication. Phys. Rev. Lett. 95 080501.
    • (2005) Phys. Rev. Lett , vol.95 , pp. 080501
    • Kraus, B.1    Gisin, N.2    Renner, R.3
  • 63
    • 33645313777 scopus 로고    scopus 로고
    • Hitting time for quantum walks on the hypercube
    • Krovi, H. and Brun, T. A. (2006a) Hitting time for quantum walks on the hypercube. Phys. Rev. A 73 (3) 032341.
    • (2006) Phys. Rev. A , vol.73 , Issue.3 , pp. 032341
    • Krovi, H.1    Brun, T.A.2
  • 64
    • 33750443251 scopus 로고    scopus 로고
    • Quantum walks with infinite hitting times
    • Krovi, H. and Brun, T. A. (2006b) Quantum walks with infinite hitting times. Phys. Rev. A 74 (4) 042334.
    • (2006) Phys. Rev. A , vol.74 , Issue.4 , pp. 042334
    • Krovi, H.1    Brun, T.A.2
  • 66
    • 26444489529 scopus 로고    scopus 로고
    • The hidden subgroup problem - review and open problems
    • ArXiv: quant-ph/0411037
    • Lomont, C. (2004) The hidden subgroup problem - review and open problems. ArXiv: quant-ph/0411037.
    • (2004)
    • Lomont, C.1
  • 67
    • 0942267739 scopus 로고    scopus 로고
    • Decoherence in quantum walks: Existence of a quantum-classical transition
    • Lopéz, C. C. and Paz, J.P. (2003) Decoherence in quantum walks: Existence of a quantum-classical transition. Phys. Rev. A 68 052305.
    • (2003) Phys. Rev. A , vol.68 , pp. 052305
    • Lopéz, C.C.1    Paz, J.P.2
  • 69
  • 70
    • 34147209344 scopus 로고    scopus 로고
    • Decoherence vs entanglement in coined quantum walks
    • Maloyer, O. and Kendon, V. (2007) Decoherence vs entanglement in coined quantum walks. New J. Phys. 9 87.
    • (2007) New J. Phys , vol.9 , pp. 87
    • Maloyer, O.1    Kendon, V.2
  • 71
    • 0030516675 scopus 로고    scopus 로고
    • From quantum cellular automata to quantum lattice gases
    • Meyer, D.A. (1996a) From quantum cellular automata to quantum lattice gases. J. Stat. Phys. 85 551-574.
    • (1996) J. Stat. Phys , vol.85 , pp. 551-574
    • Meyer, D.A.1
  • 72
    • 0000380019 scopus 로고    scopus 로고
    • On the absence of homogeneous scalar unitary cellular automata
    • Meyer, D.A. (1996b) On the absence of homogeneous scalar unitary cellular automata. Phys. Lett. A 223 (5) 337-340.
    • (1996) Phys. Lett. A , vol.223 , Issue.5 , pp. 337-340
    • Meyer, D.A.1
  • 73
    • 36749120625 scopus 로고
    • The Zeno's paradox in quantum theory
    • Misra, B. and Sudarshan, E. C. G. (1977) The Zeno's paradox in quantum theory. J. Math. Phys. 18 756.
    • (1977) J. Math. Phys , vol.18 , pp. 756
    • Misra, B.1    Sudarshan, E.C.G.2
  • 77
    • 0042481010 scopus 로고    scopus 로고
    • Quantum walk on the line
    • ArXiv: quant-ph/0010117
    • Nayak, A. and Vishwanath, A. (2000) Quantum walk on the line. ArXiv: quant-ph/0010117.
    • (2000)
    • Nayak, A.1    Vishwanath, A.2
  • 78
    • 0345862119 scopus 로고    scopus 로고
    • Families of line-graphs and their quantization
    • Pakoński, P., Tanner, G. and Życzkowski, K. (2003) Families of line-graphs and their quantization. J. Stat. Phys 111 (5/6) 1331-1352.
    • (2003) J. Stat. Phys , vol.111 , Issue.5-6 , pp. 1331-1352
    • Pakoński, P.1    Tanner, G.2    Życzkowski, K.3
  • 79
    • 27144550522 scopus 로고    scopus 로고
    • An information-theoretic security proof for QKD protocols
    • Renner, R., Gisin, N. and Kraus, B. (2005) An information-theoretic security proof for QKD protocols. Phys. Rev. A 72 012332.
    • (2005) Phys. Rev. A , vol.72 , pp. 012332
    • Renner, R.1    Gisin, N.2    Kraus, B.3
  • 80
    • 19744380823 scopus 로고    scopus 로고
    • Aperiodic quantum random walks
    • Ribeiro, P., Milman, P. and Mosseri, R. (2004) Aperiodic quantum random walks. Phys. Rev. Lett. 93 (19) 190503.
    • (2004) Phys. Rev. Lett , vol.93 , Issue.19 , pp. 190503
    • Ribeiro, P.1    Milman, P.2    Mosseri, R.3
  • 81
    • 33947591866 scopus 로고    scopus 로고
    • Richter, P. (2007a) Almost uniform sampling in quantum walks. New J. Phys. 9 72. See also ArXiv: quant-ph/0606202.
    • Richter, P. (2007a) Almost uniform sampling in quantum walks. New J. Phys. 9 72. See also ArXiv: quant-ph/0606202.
  • 82
    • 34948855496 scopus 로고    scopus 로고
    • Richter, P. (2007b) Quantum speedup of classical mixing processes. Phys. Rev. A 76 042306. See also ArXiv: quant-ph/0609204.
    • Richter, P. (2007b) Quantum speedup of classical mixing processes. Phys. Rev. A 76 042306. See also ArXiv: quant-ph/0609204.
  • 85
    • 33244477865 scopus 로고    scopus 로고
    • Experimental implementation of discrete time quantum random walk on an NMR quantum information processor
    • Ryan, C. A., Laforest, M., Boileau, J. C. and Laflamme, R. (2005) Experimental implementation of discrete time quantum random walk on an NMR quantum information processor. Phys. Rev. A 72 062317.
    • (2005) Phys. Rev. A , vol.72 , pp. 062317
    • Ryan, C.A.1    Laforest, M.2    Boileau, J.C.3    Laflamme, R.4
  • 88
    • 0013052723 scopus 로고    scopus 로고
    • A probabilistic algorithm for k-SAT and constraint satisfaction problems
    • IEEE Computer Society Press
    • Schöning, U. (1999) A probabilistic algorithm for k-SAT and constraint satisfaction problems. In: 40th Annual Symposium on FOCS, IEEE Computer Society Press 17-19.
    • (1999) 40th Annual Symposium on FOCS , pp. 17-19
    • Schöning, U.1
  • 89
    • 1342267534 scopus 로고    scopus 로고
    • On the digraph of a unitary matrix
    • Severini, S. (2003) On the digraph of a unitary matrix. SIAM J. Matrix Anal. Appl. 25 (1) 295-300.
    • (2003) SIAM J. Matrix Anal. Appl , vol.25 , Issue.1 , pp. 295-300
    • Severini, S.1
  • 90
    • 43649091074 scopus 로고    scopus 로고
    • Graphs of a unitary matrix
    • ArXiv: math.CO/0303084
    • Severini, S. (2006) Graphs of a unitary matrix. ArXiv: math.CO/0303084.
    • (2006)
    • Severini, S.1
  • 91
    • 1142292322 scopus 로고    scopus 로고
    • One dimensional quantum walk with unitary noise
    • Shapira, D., Biham, O., Bracken, A.J. and Hackett, M. (2003) One dimensional quantum walk with unitary noise. Phys. Rev. A 68 (6) 062315.
    • (2003) Phys. Rev. A , vol.68 , Issue.6 , pp. 062315
    • Shapira, D.1    Biham, O.2    Bracken, A.J.3    Hackett, M.4
  • 93
    • 0142051871 scopus 로고    scopus 로고
    • Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
    • Shor, P.W. (1997) Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Sci Statist. Comput. 26 1484.
    • (1997) SIAM J. Sci Statist. Comput , vol.26 , pp. 1484
    • Shor, P.W.1
  • 94
    • 33144466650 scopus 로고    scopus 로고
    • Continuous-time quantum walks on a cycle graph
    • Solenov, D. and Fedichkin, L. (2006a) Continuous-time quantum walks on a cycle graph. Phys. Rev. A 73 012313.
    • (2006) Phys. Rev. A , vol.73 , pp. 012313
    • Solenov, D.1    Fedichkin, L.2
  • 95
    • 33144466463 scopus 로고    scopus 로고
    • Non-unitary quantum walks on hyper-cycles
    • Solenov, D. and Fedichkin, L. (2006b) Non-unitary quantum walks on hyper-cycles. Phys. Rev. A 73 012308.
    • (2006) Phys. Rev. A , vol.73 , pp. 012308
    • Solenov, D.1    Fedichkin, L.2
  • 96
    • 33748480690 scopus 로고    scopus 로고
    • Connecting the discrete and continuous-time quantum walks
    • Strauch, F.W. (2006a) Connecting the discrete and continuous-time quantum walks. Phys. Rev. A 74 (3) 030301.
    • (2006) Phys. Rev. A , vol.74 , Issue.3 , pp. 030301
    • Strauch, F.W.1
  • 97
    • 33646894464 scopus 로고    scopus 로고
    • Relativistic quantum walks
    • Strauch, F.W. (2006b) Relativistic quantum walks. Phys. Rev. A 73 (6) 054302.
    • (2006) Phys. Rev. A , vol.73 , Issue.6 , pp. 054302
    • Strauch, F.W.1
  • 99
    • 17744399997 scopus 로고    scopus 로고
    • Spectra of quantized walks and a √δε rule
    • ArXiv: quant-ph/0401053
    • Szegedy, M. (2004b) Spectra of quantized walks and a √δε rule. ArXiv: quant-ph/0401053.
    • (2004)
    • Szegedy, M.1
  • 100
    • 33646864302 scopus 로고    scopus 로고
    • A concise guide to complex Hadamard matrices
    • Tadej, W. and Życzkowski, K. (2006) A concise guide to complex Hadamard matrices. Open Syst. Inf. Dyn. 13 133-177.
    • (2006) Open Syst. Inf. Dyn , vol.13 , pp. 133-177
    • Tadej, W.1    Życzkowski, K.2
  • 101
    • 3543017857 scopus 로고    scopus 로고
    • Implementing the quantum random walk
    • Travaglione, B. C. and Milburn, G. J. (2002) Implementing the quantum random walk. Phys. Rev. A 65 032310.
    • (2002) Phys. Rev. A , vol.65 , pp. 032310
    • Travaglione, B.C.1    Milburn, G.J.2
  • 102
    • 3042648972 scopus 로고    scopus 로고
    • Controlling discrete quantum walks: Coins and initial states
    • Tregenna, B., Flanagan, W., Maile, R. and Kendon, V. (2003) Controlling discrete quantum walks: coins and initial states. New J. Phys. 5 83.
    • (2003) New J. Phys , vol.5 , pp. 83
    • Tregenna, B.1    Flanagan, W.2    Maile, R.3    Kendon, V.4
  • 103
    • 0035278392 scopus 로고    scopus 로고
    • Quantum simulations of classical random walks and undirected graph connectivity
    • Watrous, J. (2001) Quantum simulations of classical random walks and undirected graph connectivity. J. Comp. System Sciences 62 (2) 376-391.
    • (2001) J. Comp. System Sciences , vol.62 , Issue.2 , pp. 376-391
    • Watrous, J.1
  • 104
    • 43649084723 scopus 로고    scopus 로고
    • Private communication
    • Watrous, J. (2002) Private communication.
    • (2002)
    • Watrous, J.1
  • 106
    • 84958761644 scopus 로고    scopus 로고
    • An analysis of absorbing times of quantum walks
    • Calude, C, Dinneen, M.J. and Peper, F, eds, Proceedings: Unconventional Models of Computation, Third Intl. Conf, UMC
    • Yamasaki, T., Kobayashi, H. and Imai, H. (2002) An analysis of absorbing times of quantum walks. In: Calude, C., Dinneen, M.J. and Peper, F. (eds.) Proceedings: Unconventional Models of Computation, Third Intl. Conf., UMC 2002. Springer-Verlag Lecture Notes in Computer Science 2509 315-330.
    • (2002) Springer-Verlag Lecture Notes in Computer Science , vol.2509 , pp. 315-330
    • Yamasaki, T.1    Kobayashi, H.2    Imai, H.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.