메뉴 건너뛰기




Volumn 57, Issue 6, 2010, Pages

Limitations of quantum coset states for graph isomorphism

Author keywords

Graph isomorphism; Hidden subgroup problem; Quantum algorithms; Quantum computation

Indexed keywords

AMOUNT OF INFORMATION; COMMON FEATURES; COSET STATE; GRAPH ISOMORPHISM; HIDDEN SUBGROUP PROBLEM; JOINT MEASUREMENT; POTENTIAL SOURCES; QUANTUM ALGORITHMS; QUANTUM COMPUTATION; QUANTUM MEASUREMENT; UPPER BOUND;

EID: 78649239030     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/1857914.1857918     Document Type: Article
Times cited : (29)

References (48)
  • 4
    • 33748603175 scopus 로고    scopus 로고
    • From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups
    • IEEE Computer Society Press, Los Alamitos, CA. Also: ArXiv preprint quant-ph/0504083
    • BACON, D., CHILDS, A., AND VAN DAM, W. 2005. From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups. In Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05). IEEE Computer Society Press, Los Alamitos, CA. Also: ArXiv preprint quant-ph/0504083.
    • (2005) Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)
    • Bacon, D.1    Childs, A.2    Van Dam, W.3
  • 5
    • 33748332658 scopus 로고    scopus 로고
    • Optimal measurements forthe dihedral hidden subgroup problem
    • 2006, (Also: ArXiv preprint quant-ph/0501044)
    • BACON, D., CHILDS, A., AND DAM, W. V. 2006. Optimal measurements forthe dihedral hidden subgroup problem. Chicago J. Theoret. Comput. Sci. 2006, 2, 1-25. (Also: ArXiv preprint quant-ph/0501044).
    • (2006) Chicago J. Theoret. Comput. Sci. , Issue.2 , pp. 1-25
    • Bacon, D.1    Childs, A.2    Dam, W.V.3
  • 6
    • 0030642909 scopus 로고    scopus 로고
    • Quantum computation of Fourier transforms over the symmetric groups
    • ACM, New York
    • BEALS, R. 1997. Quantum computation of Fourier transforms over the symmetric groups. In Proceedings of the Symposium on Theory of Computing (STOC'97). ACM, New York, 48-53.
    • (1997) Proceedings of the Symposium on Theory of Computing (STOC'97) , pp. 48-53
    • Beals, R.1
  • 9
    • 0030661550 scopus 로고    scopus 로고
    • An exact polynomial-time algorithm for Simon's problem
    • ISTCS, IEEE Computer Society Press, Los Alamitos, CA, (Also: ArXiv preprint quant-ph/9704027.)
    • BRASSARD, G., AND HøYER, P. 1997. An exact polynomial-time algorithm for Simon's problem. In Proceedings of 5th Israeli Symposium on Theory of Computing and Systems. ISTCS, IEEE Computer Society Press, Los Alamitos, CA, 12-33. (Also: ArXiv preprint quant-ph/9704027.)
    • (1997) Proceedings of 5th Israeli Symposium on Theory of Computing and Systems , pp. 12-33
    • Brassard, G.1    Høyer, P.2
  • 10
    • 34547539405 scopus 로고    scopus 로고
    • On the quantum hardness of solving isomorphism problems as nonabelian hidden shift problems
    • Also: ArXiv preprint quant-ph/0510185
    • CHILDS, A., AND WOCJAN, P. 2007. On the quantum hardness of solving isomorphism problems as nonabelian hidden shift problems. Quant. Inf. Comput. 7, 5&6, 371-382. (Also: ArXiv preprint quant-ph/0510185.)
    • (2007) Quant. Inf. Comput. , vol.7 , Issue.5-6 , pp. 371-382
    • Childs, A.1    Wocjan, P.2
  • 11
    • 0034288481 scopus 로고    scopus 로고
    • On quantum algorithms for noncommutative hidden subgroups
    • ETTINGER, M., AND HøYER, P. 2000. On quantum algorithms for noncommutative hidden subgroups.Adva. Appl. Math. 25, 3, 239-251.
    • (2000) Adva. Appl. Math. , vol.25 , Issue.3 , pp. 239-251
    • Ettinger, M.1    Høyer, P.2
  • 14
    • 2642588230 scopus 로고    scopus 로고
    • The quantum query complexity of the hidden subgroup problem is polynomial
    • Also: ArXiv preprint quant-ph/0401083
    • ETTINGER, M., HøYER, P., AND KNILL, E. 2004. The quantum query complexity of the hidden subgroup problem is polynomial. Information Processing Letters 91, 1, 43-48. (Also: ArXiv preprint quant-ph/0401083).
    • (2004) Information Processing Letters , vol.91 , Issue.1 , pp. 43-48
    • Ettinger, M.1    Høyer, P.2    Knill, E.3
  • 17
    • 84966248838 scopus 로고
    • Character values at involutions
    • GALLAGHER, P. X. 1994. Character values at involutions. Proc. AMS 120, 3, 657-659.
    • (1994) Proc. AMS , vol.120 , Issue.3 , pp. 657-659
    • Gallagher, P.X.1
  • 18
    • 4043084179 scopus 로고    scopus 로고
    • Quantum solution to the hidden subgroup problem for Poly-Near-Hamiltonian groups
    • GAVINS KY, D. 2004. Quantum solution to the hidden subgroup problem for Poly-Near-Hamiltonian groups. Quant. Inf. Computat. 4, 3, 229-235.
    • (2004) Quant. Inf. Computat. , vol.4 , Issue.3 , pp. 229-235
    • Gavins Ky, D.1
  • 19
    • 2542631212 scopus 로고    scopus 로고
    • Quantum mechanical algorithms forthe nonabelian hidden subgroup problem
    • GRIGNI, M., SCHULMAN, L., VAZIRANI, M., AND VAZIRANI, U. 2004. Quantum mechanical algorithms forthe nonabelian hidden subgroup problem. Combinatorica 24, 1, 137-154.
    • (2004) Combinatorica , vol.24 , Issue.1 , pp. 137-154
    • Grigni, M.1    Schulman, L.2    Vazirani, M.3    Vazirani, U.4
  • 20
    • 0029701737 scopus 로고    scopus 로고
    • A fast quantum mechanical algorithm for database search
    • ACM, New York, (Also: ArXiv preprint quant-ph/9605043.)
    • GROVER, L. 1996. A fast quantum mechanical algorithm for database search. In Proceedings of the 28th Annual ACM Symposium on Theory of Computing (STOC'96). ACM, New York, 212-219. (Also: ArXiv preprint quant-ph/9605043.)
    • (1996) Proceedings of the 28th Annual ACM Symposium on Theory of Computing (STOC'96) , pp. 212-219
    • Grover, L.1
  • 24
    • 0141534114 scopus 로고    scopus 로고
    • The hidden subgroup problem and quantum computation using group representations
    • HALLGREN, S., RUSSELL, A., AND TA-SHMA, A. 2003. The hidden subgroup problem and quantum computation using group representations. SIAM J. Comput. 32, 4, 916-934.
    • (2003) SIAM J. Comput. , vol.32 , Issue.4 , pp. 916-934
    • Russella., H.S.1    Ta-Shma, A.2
  • 26
    • 20744439021 scopus 로고    scopus 로고
    • Efficient quantum algorithms for some instances of the non-Abelian hidden subgroup problem
    • Also: ArXiv preprint quant-ph/0102014
    • IVANYOS, G., MAGNIEZ, F., AND SANTHA, M. 2003. Efficient quantum algorithms for some instances of the non-Abelian hidden subgroup problem. Int. J. Foundations of Computer Science 14, 5, 723-740. (Also: ArXiv preprint quant-ph/0102014.)
    • (2003) Int. J. Foundations of Computer Science , vol.14 , Issue.5 , pp. 723-740
    • Ivanyos, G.1    Magniez, F.2    Santha, M.3
  • 27
    • 38049170875 scopus 로고    scopus 로고
    • An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups
    • Lecture Notes in Computer Science, Springer- Verlag, Berlin, Germany, (Also: ArXiv preprint quant-ph/0701235.)
    • IVANYOS, G., SANSELME, L., AND SANTHA, M. 2007. An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups. In Proceedings of the 24th Annual Symposium on Theoretical Aspects of Computer Science (STACS'07). Lecture Notes in Computer Science, vol. 4393. Springer- Verlag, Berlin, Germany, 586-597. (Also: ArXiv preprint quant-ph/0701235.)
    • (2007) Proceedings of the 24th Annual Symposium on Theoretical Aspects of Computer Science (STACS'07) , vol.4393 , pp. 586-597
    • Ivanyos, G.1    Sanselme, L.2    Santha, M.3
  • 31
    • 33644591453 scopus 로고    scopus 로고
    • A subexponential-time quantum algorithm for the dihedral hidden subgroup problem
    • Also arxiv preprint quant-ph/0302112
    • KUPERBERG, G. 2005. A subexponential-time quantum algorithm for the dihedral hidden subgroup problem. SIAM J. Comput. 35, 1, 170-188. (Also arxiv preprint quant-ph/0302112.)
    • (2005) SIAM J. Comput. , vol.35 , Issue.1 , pp. 170-188
    • Kuperberg, G.1
  • 32
    • 84950854506 scopus 로고
    • 2 over a finite field and related numerical experiments
    • 2 over a finite field and related numerical experiments. Exp. Math. 1, 2, 115-139.
    • (1992) Exp. Math. , vol.1 , Issue.2 , pp. 115-139
    • Lafferty, J.D.1    Rockmore, D.2
  • 33
    • 46449095796 scopus 로고    scopus 로고
    • The power of strong Fourier sampling: Quantum algorithms for affine groups and hidden shifts
    • Also: ArXiv preprint quant-ph/0503095
    • MOORE, C., ROCKMORE, D., RUSSELL, A., AND SCHULMAN, L. 2007a. The power of strong Fourier sampling: quantum algorithms for affine groups and hidden shifts. SIAM J. Comput. 37, 3, 938-958. (Also: ArXiv preprint quant-ph/0503095.)
    • (2007) SIAM J. Comput. , vol.37 , Issue.3 , pp. 938-958
    • Moore, C.1    Rockmore, D.2    Russell, A.3    Schulman, L.4
  • 39
    • 84961385953 scopus 로고    scopus 로고
    • The hidden subgroup problem and eigenvalue estimation on a quantum computer
    • Lecture Notes in Computer Science, Springer-Verlag, Berlin, Germany
    • MOSCA, M., AND EKERT, A. 1998. The hidden subgroup problem and eigenvalue estimation on a quantum computer. In Quantum Computing and Quantum Communications. Lecture Notes in Computer Science, vol. 1509. Springer-Verlag, Berlin, Germany, 174-188.
    • (1998) Quantum Computing and Quantum Communications , vol.1509 , pp. 174-188
    • Mosca, M.1    Ekert, A.2
  • 41
    • 67650692745 scopus 로고    scopus 로고
    • Random measurement bases, quantum state distinction and applications to the hidden subgroup problem
    • Also: ArXiv preprints quant-ph/0503114 and quant-ph/0512085
    • RADHAKRISHNAN, J., RÖTTELER, M., AND SEN, P. 2009. Random measurement bases, quantum state distinction and applications to the hidden subgroup problem. Algorithmica 55, 3, 490-516. (Also: ArXiv preprints quant-ph/0503114 and quant-ph/0512085.)
    • (2009) Algorithmica , vol.55 , Issue.3 , pp. 490-516
    • Radhakrishnan, J.1    Rötteler, M.2    Sen, P.3
  • 42
    • 20444451186 scopus 로고    scopus 로고
    • New lattice-based cryptographic constructions
    • REGEV, O. 2004a. New lattice-based cryptographic constructions. J. ACM 51, 6, 899-942.
    • (2004) J ACM , vol.51 , Issue.6 , pp. 899-942
    • Regev, O.1
  • 43
    • 3142689917 scopus 로고    scopus 로고
    • Quantum computation and lattice problems
    • REGEV, O. 2004b. Quantum computation and lattice problems. SIAM J. Comput. 33, 2, 738-760.
    • (2004) SIAM J. Comput. , vol.33 , Issue.2 , pp. 738-760
    • Regev, O.1
  • 44
    • 0030502729 scopus 로고    scopus 로고
    • Upper bound on the characters of the symmetric groups
    • ROICHMAN, Y. 1996. Upper bound on the characters of the symmetric groups. Invent. Math. 125, 451485.
    • (1996) Invent. Math. , vol.125 , pp. 451485
    • Roichman, Y.1
  • 47
    • 0142051871 scopus 로고    scopus 로고
    • Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
    • SHOR, P. 1997. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 5, 1484-1509.
    • (1997) SIAM J. Comput. , vol.26 , Issue.5 , pp. 1484-1509
    • Shor, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.