Decomposing finite Abelian groups

Quantum Information and Computation

Volumn 1, Issue 3, 2001, Pages 26-32

  Cheung, Kevin K H ^a   Mosca, Michele ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Abelian groups; Algorithm; Quantum

Indexed keywords

ALGORITHMS; QUANTUM EFFICIENCY; QUANTUM THEORY;

ABELIAN GROUP; CLASS NUMBERS; CYCLIC GROUP; QUANTUM; QUANTUM ALGORITHMS; RIEMANN HYPOTHESIS;

GROUP THEORY;

EID: 0012577258     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (13)

1. P. W Shor (1997), Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM J. Comput., 26, pp. 1484-1509.
2. U. Vazirani (1997), UC Berkeley Course CS294-2 Quantum Computation Fall 1997. Lecture notes last downloaded on June 21, 2001 from http://www.cs.berkeley.edu/~vazirani/qc.html.
3. P. Høyer (1999), Conjugated operators in quantum algorithms, Phys. Rev. A, 59, pp. 3280-3289.
4. M. Mosca and A. Ekert (1999), The hidden subgroup problem and eigenvalue estimation on a quantum computer, in C. P. Williams, editor, Proceedings of the 1st NASA International Conference on Quantum Computing and Quantum Communication, Palm Springs, USA, Lecture Notes in Computer Science, 1509, pp. 174-188, Springer (Berlin).
5. M. Mosca (1999), Quantum Computer Algorithms, D. Phil Thesis, University of Oxford.
6. J. Watrous (2001), Quantum algorithms for solvable groups, Proceedings of the 33rd ACM Symposium on Theory of Computing, pp. 60-67.
7. H. Cohen (1993), A Course in Computational Algebraic Number Theory, Springer-Verlag (Berlin).
8. M. Jacobson (1999), Subexponential Class Group Computation in Quadratic Orders, Doctoral Thesis, TU Darmstadt.
9. J. A. Beachy and W. D. Blair (1990), Abstract algebra with a concrete introduction, Prentice-Hall Inc. (New Jersey).
10. A. Schrijver (1986), Theory of Linear and Integer Programming, Wiley and Sons (England).
11. R. Kannan and A. Bachem (1979), Polynomial algorithms for computing the Smith and Hermite normal forms of an integer matrix, SIAM J. Comput., 8, pp. 499-507.
12. H. Cohen (1991), Advanced Topics in Computational Number Theory, Springer-Verlag (New York).
13. D. Bonch and R. J. Lipton (1995), Quantum cryptanalysis of hidden linear functions (extended abstract), in D. Coppersmith, editor, Advances in Cryptology: CRYPTO 95, Lecture Notes on Computer Science, 963, pp. 424-437, Springer (Berlin).