The quantum query complexity of the determinant

Information Processing Letters

Volumn 109, Issue 6, 2009, Pages 325-328

  Dörn, Sebastian ^a   Thierauf, Thomas ^b  

^a UNIVERSITY OF ULM   (Germany)

^b Fak Elektronik und Informatik   (Germany)

Author keywords

Computational complexity; Determinant; Matrix power; Quantum query complexity

Indexed keywords

ALGEBRA; INVERSE PROBLEMS;

DETERMINANT; LINEAR ALGEBRA PROBLEMS; MATRIX INVERSE; MATRIX POWER; MATRIXES; POWER PROBLEMS; QUANTUM QUERIES; QUANTUM QUERY COMPLEXITY;

COMPUTATIONAL COMPLEXITY;

EID: 58849150248     PISSN: 00200190     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ipl.2008.11.006     Document Type: Article

References (21)

1. Ambainis A. Quantum lower bounds by quantum arguments. Journal of Computer and System Sciences 64 (2002) 750-767
2. A. Ambainis, Quantum walk algorithm for element distinctness, in: Proceedings of FOCS'04, 2004, pp. 22-31
3. A. Ambainis, R. Špalek, Quantum algorithms for matching and network flows, in: Proceedings of STACS'06, 2006, pp. 172-183
4. Beals R., Buhrman H., Cleve R., Mosca M., and de Wolf R. Quantum lower bounds by polynomials. Journal of ACM 48 (2001) 778-797
5. A. Berzina, A. Dubrovsky, R. Freivalds, L. Lace, O. Scegulnaja, Quantum query complexity for some graph problems, in: Proceedings of SOFSEM'04, 2004, pp. 140-150
6. H. Buhrman, C. Dürr, M Heiligman, P. Høyer, F. Magniez, M. Santha, R. de Wolf, Quantum algorithms for element distinctness, in: Proceedings of CCC'01, 2001, pp. 131-137
7. G. Brassard, P. Høyer, A. Tapp, Quantum cryptanalysis of hash and claw-free functions, in: Proceedings of LATIN'98, 1998, pp. 163-169
8. H. Buhrman, R. Špalek, Quantum verification of matrix products, in: Proceedings of SODA'06, 2006, pp. 880-889
9. Brualdi R., and Ryser H. Combinatorial Matrix Theory. Encyclopedia of Mathematics and its Applications vol. 39 (1991), Cambridge University Press
10. Cvetković D., Doob M., and Sachs H. Spectra of Graphs, Theory and Application (1980), Academic Press
11. C. Dürr, M. Heiligman, P. Høyer, M. Mhalla, Quantum query complexity of some graph problems, in: Proceedings of ICALP'04, 2004, pp. 481-493
12. S. Dörn, Quantum complexity bounds of independent set problems, in: Proceedings of SOFSEM'07 (SRF), 2007, pp. 25-36
13. S. Dörn, Quantum algorithms for graph traversals and related problems, in: Proceedings of CIE'07, 2007, pp. 123-131
14. S. Dörn, T. Thierauf, The quantum query complexity of algebraic properties, in: Proceedings of FCT'07, 2007, pp. 250-260
15. S. Dörn, T. Thierauf, The quantum complexity of group testing, in: Proceedings of SOFSEM'08, 2008, pp. 506-518
16. F. Magniez, A. Nayak, Quantum complexity of testing group commutativity, in: Proceedings of ICALP'05, 2005, pp. 1312-1324
17. F. Magniez, M. Santha, M. Szegedy, Quantum algorithms for the triangle problem, in: Proceedings of SODA'05, 2005, pp. 1109-1117
18. Mahajan M., and Vinay V. Determinant: Combinatorics, algorithms, and complexity. Chicago Journal of Theoretical Computer Science 1997 5 (1997)
19. Mahajan M., and Vinay V. Determinant: Old algorithms, new insights. SIAM Journal on Discrete Mathematics 12 4 (1999) 474-490
20. Zeilberger D. A combinatorial approach to matrix algebra. Discrete Mathematics 56 (1985) 61-72
21. Zhang S. On the power of Ambainis's lower bounds. Proceedings of ICALP'04. Lecture Notes in Computer Science vol. 3142 (2004) 1238-1250