Exponential algorithmic speedup by a quantum walk

Conference Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2003, Pages 59-68

  Childs, Andrew M ^a   Cleve, Richard ^b   Deotto, Enrico ^a   Farhi, Edward ^a   Gutmann, Sam ^c   Spielman, Daniel A ^d  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF CALGARY   (Canada)

^c NORTHEASTERN UNIVERSITY   (United States)

^d MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Quantum algorithms; Quantum walks

Indexed keywords

ALGORITHMS; FOURIER TRANSFORMS; GRAPH THEORY; PROBLEM SOLVING;

QUANTUM WALK;

QUANTUM THEORY;

EID: 0038784710     PISSN: 07349025     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/780551.780552     Document Type: Conference Paper

References (30)

1. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
2. D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani. Quantum walks on graphs. In Proc. of the 33rd ACM Symp. on Theory of Computing, pages 50-59, 2001.
3. D. Aharonov and A. Ta-Shma. Adiabatic quantum state generation and statistical zero knowledge. In Proc. 35th ACM Symp. on Theory of Computing, 2003.
4. A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, and J. Watrous. One-dimensional quantum walks. In Proc. 33rd ACM Symp. on Theory of Computing, pages 37-49, 2001.
5. J. N. de Beaudrap, R. Cleve, and J. Watrous. Sharp quantum vs. classical query complexity separations. Algorithmica, 34:449-461, 2002.
6. E. Bernstein and U. Vazirani. Quantum complexity theory. SIAM J. on Computing, 26:1411-1473, 1997.
7. A. M. Childs, E. Farhi, and S. Gutmann. An example of the difference between quantum and classical random walks. Quantum Information Processing, 1:35-43, 2002.
8. W. van Dam and S. Hallgren. Efficient quantum algorithms for shifted quadratic character problems. quant-ph/0011067.
9. W. van Dam and G. Seroussi. Efficient quantum algorithms for estimating Gauss sums. Unpublished.
10. D. Deutsch. Quantum theory, the Church-Turing principle, and the universal quantum computer. Proc. Roy. Soc. London A, 400:96-117, 1985.
11. D. Deutsch and R. Jozsa. Rapid solution of problems by quantum computation. Proc. Roy. Soc. London A, 439:553-558, 1992.
12. E. Farhi and S. Gutmann. Quantum computation and decision trees. Phys. Rev. A, 58:915-928, 1998.
13. J. Goldstone. Personal communication, Sept. 2002.
14. M. Grigni, L. Schulman, M. Vazirani, and U. Vazirani. Quantum mechanical algorithms for the nonabelian hidden subgroup problem. In Proc. 33rd ACM Symp. on Theory of Computing, pages 68-74, 2001.
15. S. Hallgren. Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem. In Proc. 34th ACM Symp. on Theory of Computing, pages 653-658, 2002.
16. S. Hallgren, A. Russell, and A. Ta-Shma. Normal subgroup reconstruction and quantum computation using group representations. In Proc. 32nd ACM Symp. on Theory of Computing, pages 627-635, 2000.
17. G. Ivanos, F. Magniez, and M. Santha. Efficient quantum algorithms for some instances of the non-abelian hidden subgroup problem. quant-ph/0102014.
18. J. Kempe. Quantum random walks hit exponentially faster. quant-ph/0205083.
19. A. Kitaev. Quantum measurements and the abelian stabilizer problem, quant-ph/9511026.
20. S. Lloyd. Universal quantum simulators, Science 273:1073-1078, 1996.
21. D. A. Meyer. From quantum cellular automata to quantum lattice gasses. J. Stat. Phys., 85:551-574, 1996.
22. C. Moore and A. Russell. Quantum walks on the hypercube. In Proc. of RANDOM 02, Vol. 2483 of LNCS, pages 164-178, 2002.
23. M. Mosca and A. Ekert. The hidden subgroup problem and eigenvalue estimation on a quantum computer. In Proc. 1st NASA International Conf. on Quantum Computing and Quantum Communication, Vol. 1509 of LNCS, pages 174-188, 1999.
24. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
25. P. W. Shor. Algorithms for quantum computation: discrete logarithms and factoring. SIAM J. on Computing, 26:1484-1509, 1997.
26. D. Simon. On the power of quantum computation. SIAM J. on Computing, 26:1474-1483, 1997.
27. V. G. Vizing. On an estimate of the chromatic class of a p-graph. Metody Diskret. Analiz., 3:25-30, 1964.
28. J. Watrous. Quantum algorithms for solvable groups. In Proc. 33rd ACM Symposium on Theory of Computing, pages 60-67, 2001.
29. J. Watrous. Quantum simulations of classical random walks and undirected graph connectivity. J. Computer and System Sciences, 62:376-391, 2001.
30. A. Wigderson. The complexity of graph connectivity. In Proc. 17th Mathematical Foundations of Computer Science Conf., Vol. 629 of LNCS, pages 112-132, 1992.