Quantum mechanical algorithms for the nonabelian hidden subgroup problem

Combinatorica

Volumn 24, Issue 1, 2004, Pages 137-154

  Grigni, Michelangelo ^a   Schulman, Leonard J ^c   Vazirani, Monica ^b   Vazirani, Umesh ^d  

^a EMORY UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2542631212     PISSN: 02099683     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00493-004-0009-8     Document Type: Article

References (16)

1. R. BAER: Gruppen mit Hamiltonischem Kern, Compositio Math. 2 (1935), 241-246.
2. ROBERT BEALS: Quantum computation of Fourier transforms over symmetric groups, In Proceedings of the 29th Annual ACM Symposium on Theory of Computing (1997), 48-53.
3. R. A. BRYCE: The subgroups of Baer and Hughes, Arch. Math. 61 (1993), 305-312.
4. MICHAEL CLAUSEN: Fast generalized Fourier transforms, Theor. Comp. Sci. 67 (1989), 55-63.
5. PERSI DIACONIS and DANIEL ROCKMORE: Efficient computation of the Fourier transform of finite groups, J. Amer. Math. Soc. 3(2) (1990), 297-332.
6. MARK ETTINGER and PETER HØYER: On quantum algorithms for noncommutative hidden subgroups, Advances in Applied Mathematics 25(3) (2000), 239-251. (LANL preprint quant-ph/9807029, 1998.)
7. MARK ETTINGER, PETER HØYER and EMANUEL KNILL: Hidden subgroup states are almost orthogonal, LANL preprint quant-ph/9901034.
8. SEAN HALLOREN, ALEXANDER RUSSELL and AMNON TA-SHMA: Normal subgroup reconstruction and quantum computation using group representations, In Proceedings of the 32nd Annual ACM Symposium on Theory of Computing (2000), 627-635.
9. ALEXEI KITAEV: Quantum measurements and the abelian stabilizer problem, ECCC Report TR96-003, 1996.
10. JOHANNES KÖHLER, UWE SCHÖNING and JACOBO TORÁN: The Graph Isomorphism Problem: Its Structural Complexity, Birkhäuser, 1993.
11. MARKUS PÜSCHEL, MARTIN RÖTTELER and THOMAS BETH: Fast quantum Fourier transforms for a class of non-abelian groups, LANL e-preprint quant-ph/9807064, 1998.
12. DANIEL ROCKMORE: Computation of Fourier Transforms on the Symmetric Group, in: E. Kaltofen, S. M. Watt (eds.), Computers and Mathematics, Springer, 1989.
13. JEAN-PIERRE SERRE: Linear Representations of Finite Groups, Springer-Verlag, 1977.
14. PETER SHOR: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing 26(5) (1997), 1484-1509.
15. DANIEL SIMON: On the power of quantum computation, SIAM Journal on Computing 26(5) (1997), 1474-1483.
16. WIM VAN DAM and SEAN HALLGREN: Efficient Quantum Algorithms for Shifted Quadratic Character Problems, LANL e-preprint quant-ph/0011067, 2000.