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Volumn 2006, Issue , 2006, Pages 274-287

Random measurement bases, quantum state distinction and applications to the hidden subgroup problem

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; FOURIER TRANSFORMS; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING; RANDOM PROCESSES; VARIATIONAL TECHNIQUES;

EID: 34247498307     PISSN: 10930159     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CCC.2006.37     Document Type: Conference Paper
Times cited : (36)

References (24)
  • 1
    • 33748603175 scopus 로고    scopus 로고
    • From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups
    • Also arxiv preprint quant-ph/0504083
    • D. Bacon, A. Childs, and W. van Dam. 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, 2005. Also arxiv preprint quant-ph/0504083.
    • (2005) Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
    • Bacon, D.1    Childs, A.2    van Dam, W.3
  • 2
    • 33748332658 scopus 로고    scopus 로고
    • Optimal measurements for the dihedral hidden subgroup problem
    • Arxiv preprint quant-ph/0501044
    • D. Bacon, A. Childs, and W. van Dam. Optimal measurements for the dihedral hidden subgroup problem. Arxiv preprint quant-ph/0501044, 2005.
    • (2005)
    • Bacon, D.1    Childs, A.2    van Dam, W.3
  • 3
    • 0035981791 scopus 로고    scopus 로고
    • Reversing quantum dynamics with near-optimal quantum and classical fidelity
    • Also quant-ph/0004088
    • H. Barnum and E. Knill. Reversing quantum dynamics with near-optimal quantum and classical fidelity. Journal of Mathematical Physics, 43(5):2097-2106, 2002. Also quant-ph/0004088.
    • (2002) Journal of Mathematical Physics , vol.43 , Issue.5 , pp. 2097-2106
    • Barnum, H.1    Knill, E.2
  • 4
    • 0034288481 scopus 로고    scopus 로고
    • On quantum algorithms for noncommutative hidden subgroups
    • M. Ettinger and P. Høyer. On quantum algorithms for noncommutative hidden subgroups. Advances in Applied Mathematics, 25(3):239-251, 2000.
    • (2000) Advances in Applied Mathematics , vol.25 , Issue.3 , pp. 239-251
    • Ettinger, M.1    Høyer, P.2
  • 5
    • 25644449834 scopus 로고    scopus 로고
    • Convergence conditions for random quantum circuits
    • Arxiv preprint quant-ph/0503210
    • J. Emerson, E. Livine, and S. Lloyd. Convergence conditions for random quantum circuits. Arxiv preprint quant-ph/0503210,2005.
    • (2005)
    • Emerson, J.1    Livine, E.2    Lloyd, S.3
  • 6
    • 0345731469 scopus 로고    scopus 로고
    • Pseudo-random unitary operators for quantum information processing
    • J. Emerson, Y. Weinstein, M. Saraceno, S. Lloyd, and D. Cory. Pseudo-random unitary operators for quantum information processing. Science, 302:2098-2100, 2003.
    • (2003) Science , vol.302 , pp. 2098-2100
    • Emerson, J.1    Weinstein, Y.2    Saraceno, M.3    Lloyd, S.4    Cory, D.5
  • 8
    • 2542631212 scopus 로고    scopus 로고
    • Quantum mechanical algorithms for the nonabelian hidden subgroup problem
    • M. Grigni, L. Schulman, M. Vazirani, and U. Vazirani. Quantum mechanical algorithms for the nonabelian hidden subgroup problem. Combinatorica, pages 137-154, 2004.
    • (2004) Combinatorica , pp. 137-154
    • Grigni, M.1    Schulman, L.2    Vazirani, M.3    Vazirani, U.4
  • 9
    • 24144474939 scopus 로고    scopus 로고
    • G. Gutoski and J. Watrous. Quantum interactive proofs with competing provers. In Proceedings of the 22nd Annual Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, 3404, pages 605-616. Springer-Verlag, 2005. Also arxiv preprint cs.CC/0412102.
    • G. Gutoski and J. Watrous. Quantum interactive proofs with competing provers. In Proceedings of the 22nd Annual Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, vol. 3404, pages 605-616. Springer-Verlag, 2005. Also arxiv preprint cs.CC/0412102.
  • 10
    • 0141534114 scopus 로고    scopus 로고
    • The hidden subgroup problem and quantum computation using group representations
    • S. Hallgren, A. Russell, and A. Ta-Shma. The hidden subgroup problem and quantum computation using group representations. SIAM Journal on Computing, 32(4):916-934, 2003.
    • (2003) SIAM Journal on Computing , vol.32 , Issue.4 , pp. 916-934
    • Hallgren, S.1    Russell, A.2    Ta-Shma, A.3
  • 11
    • 0000229839 scopus 로고
    • A 'pretty good' measurement for distinguishing quantum states
    • P. Hausladen and W. Wootters. A 'pretty good' measurement for distinguishing quantum states. Journal of Modern Optics, 41:2385-2390, 1994.
    • (1994) Journal of Modern Optics , vol.41 , pp. 2385-2390
    • Hausladen, P.1    Wootters, W.2
  • 12
    • 34247507325 scopus 로고    scopus 로고
    • Personal communication, March
    • A. Harrow and A. Winter. Personal communication, March 2006.
    • (2006)
    • Harrow, A.1    Winter, A.2
  • 13
    • 34247477320 scopus 로고    scopus 로고
    • Distinguishing sets of quantum states
    • Arxiv preprint quant-ph/0506205
    • R. Jain. Distinguishing sets of quantum states. Arxiv preprint quant-ph/0506205, 2005.
    • (2005)
    • Jain, R.1
  • 16
    • 33748621936 scopus 로고    scopus 로고
    • For distinguishing conjugate hidden subgroups, the pretty good measurement is as good as it gets
    • Arxiv preprint quant-ph/0501177
    • C. Moore and A. Russell. For distinguishing conjugate hidden subgroups, the pretty good measurement is as good as it gets. Arxiv preprint quant-ph/0501177, 2005.
    • (2005)
    • Moore, C.1    Russell, A.2
  • 17
    • 1842538776 scopus 로고    scopus 로고
    • C. Moore, D. Rockmore, A. Russell, and L. Schulman. The power of basis selection in Fourier sampling: Hidden subgroup problems in affine groups. In Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1113-1122, 2004. Journal version in preparation. Also arxiv preprint quant-ph/0503095.
    • C. Moore, D. Rockmore, A. Russell, and L. Schulman. The power of basis selection in Fourier sampling: Hidden subgroup problems in affine groups. In Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1113-1122, 2004. Journal version in preparation. Also arxiv preprint quant-ph/0503095.
  • 20
    • 26444514403 scopus 로고    scopus 로고
    • J. Radhakrishnan, M. Rötteler, and P. Sen. On the power of random bases in Fourier sampling: Hidden subgroup problem in the Heisenberg group. In Proceedings of the 32nd International Colloquium on Automata, Languages and. Programming, Lecture Notes in Computer Science, 3580, pages 1399-1411. Springer-Verlag, 2005. Also arxiv preprint quant-ph/0503114.
    • J. Radhakrishnan, M. Rötteler, and P. Sen. On the power of random bases in Fourier sampling: Hidden subgroup problem in the Heisenberg group. In Proceedings of the 32nd International Colloquium on Automata, Languages and. Programming, Lecture Notes in Computer Science, vol. 3580, pages 1399-1411. Springer-Verlag, 2005. Also arxiv preprint quant-ph/0503114.
  • 21
    • 0003535571 scopus 로고
    • Linear representations of finite groups
    • Springer-Verlag
    • J-P. Serre. Linear representations of finite groups. Graduate Texts in Mathematics. Springer-Verlag, 1977.
    • (1977) Graduate Texts in Mathematics
    • Serre, J.-P.1
  • 22
    • 34250127077 scopus 로고
    • Refinement of the upper bound of the constant in the central limit theorem
    • I. Shiganov. Refinement of the upper bound of the constant in the central limit theorem. Journal of Soviet Mathematics, pages 2545-2550, 1986.
    • (1986) Journal of Soviet Mathematics , pp. 2545-2550
    • Shiganov, I.1
  • 23
    • 0142051871 scopus 로고    scopus 로고
    • Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
    • P. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing, 26(5): 1484-1509, 1997.
    • (1997) SIAM Journal on Computing , vol.26 , Issue.5 , pp. 1484-1509
    • Shor, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.