On the hitting times of quantum versus random walks

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2009, Pages 86-95

  Magniez, Frédéric ^a   Nayak, Ashwin ^b   Richter, Peter C ^a   Santha, Miklos ^a,c  

^a UFR 919 Laboratoire d'Informatique Pour la Mécanique et les Sciences de l'Ingénieur   (France)

^b UNIVERSITY OF WATERLOO   (Canada)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

MARKOV PROCESSES;

DETECTION ALGORITHM; ERGODIC MARKOV CHAINS; FINDING ALGORITHM; PHASE ESTIMATION; QUANTUM ALGORITHMS; QUANTUM HITTING TIME; SQUARE ROOTS; TIME COMPLEXITY;

QUANTUM THEORY;

EID: 70349146227     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611973068.10     Document Type: Conference Paper

References (19)

1. S. Aaronson and A. Ambainis. Quantum search of spatial regions. Theory of Computing, 1(4):47-79, 2005.
2. D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani. Quantum walks on graphs. In Proceedings of the 33rd ACM Symposium on Theory of Computing, pages 50-59, 2001.
3. A. Ambainis. Quantum walks and their algorithmic applications. International Journal of Quantum Information, 1:507-518, 2003.
4. A. Ambainis. Quantum walk algorithm for Element Distinctness. In Proceedings of the 45th Symposium on Foundations of Computer Science, pages 22-31, 2004. (Pubitemid 40575263)
5. A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, and J. Watrous. One-dimensional quantum walks. In Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, pages 37-49, 2001.
6. A. Ambainis, J. Kempe, and A. Rivosh. Coins make quantum walks faster. In Proceedings of the 16th ACM-SIAM Symposium on Discrete Algorithms, pages 1099-1108, 2005.
7. H. Buhrman and R. Spalek. Quantum verification of matrix products. In Proceedings of the 17th ACM-SIAM Symposium on Discrete Algorithms, pages 880-889, 2006.
8. A. Childs and J. Goldstone. Spatial search and the Dirac equation. Physical Review A, 70:042312, 2004.
9. R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca. Quantum algorithms revisited. Proceedings of the Royal Society of London, Series A, 454:339-354, 1998.
10. L. Grover. A fast quantum mechanical algorithm for database search. In Proceedings of the 28th ACM Symposium on the Theory of Computing, pages 212-219, 1996.
11. A. Kitaev. Quantum measurements and the Abelian stabilizer problem. ECCC technical report 96-003 and arXiv.org e-print quant-ph/9511026, 1995.
12. F. Magniez and A. Nayak. Quantum complexity of testing group commutativity. Algorithmica, 48(3):221-232, 2007.
13. F. Magniez, A. Nayak, J. Roland, and M. Santha. Search via quantum walk. In Proceedings of the 39th ACM Symposium on Theory of Computing, pages 575-584, 2007.
14. F. Magniez, M. Santha, and M. Szegedy. Quantum algorithms for the triangle problem. SIAM Journal on Computing, 37(2):611-629, 2007.
15. A. Nayak and A. Vishwanath. Quantum walk on the line. Technical Report quant-ph/0010117, arXiv, 2000.
16. M. Santha. Quantum walk based search algorithms. In Proceedings of the 5th Conference on Theory and Applications of Models of Computation, volume 4978, pages 31-46. LNCS, 2008.
17. N. Shenvi, J. Kempe, and K. Whaley. A quantum random walk search algorithm. Physical Review A, 67:052307, 2003.
18. M. Szegedy. Quantum speed-up of Markov chain based algorithms. In Proceedings of the 45th Symposium on Foundations of Computer Science, pages 32-41, 2004. (Pubitemid 40575264)
19. A. Tulsi. Faster quantum walk algorithm for the two dimensional spatial search. Physical Review A, 78:012310, 2008.