Optimal computation with non-unitary quantum walks

Theoretical Computer Science

Volumn 394, Issue 3, 2008, Pages 187-196

  Kendon, Viv ^a   Maloyer, Olivier ^a,b  

^a UNIVERSITY OF LEEDS   (United Kingdom)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Quantum algorithms; Quantum computing; Quantum walks

Indexed keywords

ALGORITHMS; NUMERICAL METHODS; OPTIMIZATION; RANDOM PROCESSES;

QUANTUM ALGORITHMS; QUANTUM CORRELATIONS; QUANTUM WALKS; RANDOM BITS; RANDOM DYNAMICS;

QUANTUM COMPUTERS;

EID: 40649101864     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2007.12.011     Document Type: Article

References (33)

1. Grover L.K. Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79 (1997) 325
2. Shor P.W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Sci Statist. Comput. 26 (1997) 1484
3. Jerrum M., Sinclair A., and Vigoda E. A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries. Proc. 33rd Annual ACM STOC, ACM, NY (2001) 712-721
4. Schöning U. A probabilistic algorithm for k-SAT and constraint satisfaction problems. 40th Annual Symposium on FOCS, IEEE, Los Alamitos, CA (1999) 17-19
5. A. Nayak, A. Vishwanath, Quantum walk on the line, extended abstract, (2000) arXiv:quant-ph/0010117
6. Ambainis A., Bach E., Nayak A., Vishwanath A., and Watrous J. One-dimensional quantum walks. Proc. 33rd Annual ACM STOC, ACM, NY (2001) 60-69
7. Aharonov D., Ambainis A., Kempe J., and Vazirani U. Quantum walks on graphs. Proc. 33rd Annual ACM STOC, ACM, NY (2001) 50-59
8. Shenvi N., Kempe J., and Birgitta Whaley K. A quantum random walk search algorithm. Phys. Rev. A 67 (2003) 052307
9. Childs A.M., Cleve R., Deotto E., Farhi E., Gutmann S., and Spielman D.A. Exponential algorithmic speedup by a quantum walk. Proc. 35th Annual ACM STOC, ACM, NY (2003) 59-68
10. Ambainis A. Quantum walk algorithms for element distinctness. 45th Annual IEEE Symposium on Foundations of Computer Science, Oct. 17-19, 2004 (2004), IEEE Computer Society Press, Los Alamitos, CA 22-31
11. Kempe J. Quantum random walk algorithms. Contemp. Phys. 44 3 (2003) 302-327
12. Kendon V., and Tregenna B. Decoherence can be useful in quantum walks. Phys. Rev. A 67 (2003) 042315
13. Richter P. Almost uniform sampling in quantum walks. New J. Phys. 9 (2007) 72
14. P. Richter, Quantum speedup of classical mixing processes, (2006) arXiv:quant-ph/0609204
15. Kendon V. Decoherence in quantum walks-a review. Math. Struct. in Comp. Sci. 17 6 (2007) 1169-1220 Published online by Cambridge University Press 23 Nov 2007
16. Farhi E., and Gutmann S. Quantum computation and decison trees. Phys. Rev. A 58 (1998) 915-928
17. Bach E., Coppersmith S., Goldschen M.P., Joynt R., and Watrous J. One-dimensional quantum walks with absorbing boundaries. J. Comput. Syst. Sci. 69 4 (2004) 562-592
18. Mackay T.D., Bartlett S.D., Stephenson L.T., and Sanders B.C. Quantum walks in higher dimensions. J. Phys. A: Math. Gen. 35 (2002) 2745
19. Tregenna B., Flanagan W., Maile R., and Kendon V. Controlling discrete quantum walks: coins and initial states. New J. Phys. 5 (2003) 83
20. Krovi H., and Brun T.A. Quantum walks with infinite hitting times. Phys. Rev. A 74 4 (2006) 042334
21. Aharonov Y., Davidovich L., and Zagury N. Quantum random walks. Phys. Rev. A 48 2 (1992) 1687-1690
22. Kendon V.M., and Sanders B.C. Complementarity and quantum walks. Phys. Rev. A 71 (2004) 022307
23. Brun T.A., Carteret H.A., and Ambainis A. Quantum random walks with decoherent coins. Phys. Rev. A 67 (2003) 032304
24. O. Maloyer, V. Kendon, Decoherence vs entanglement in coined quantum walks (2007)
25. Gottesman D. A theory of fault-tolerant quantum computation. Phys. Rev. A 57 (1998) 127
26. Peres A. Separability criterion for density matrices. Phys. Rev. Lett. 77 (1996) 1413-1415
27. Horodecki M., Horodecki P., and Horodecki R. Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223 (1996) 1
28. Vidal G., and Werner R.F. A computable measure of entanglement. Phys. Rev. A 65 (2002) 032314
29. Horodecki M., Horodecki P., and Horodecki R. Mixed-state entanglement and distillation: is there a bound entanglement in nature?. Phys. Rev. Lett. 80 (1998) 5239-5242
30. Zyczkowski K. On the volume of the set of mixed entangled states II. Phys. Rev. A 60 (1999) 3496-3507
31. Carneiro I., Loo M., Xu X., Girerd M., Kendon V.M., and Knight P.L. Entanglement in coined quantum walks on regular graphs. New J. Phys. 7 (2005) 56. arXiv:quant-ph/0504042
32. Bennett C.H., Shor P.W., Smolin J.A., and Thapliyal A.V. Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem. IEEE Trans. on Info. Theory 48 10 (2002) 2637-2655
33. R. Jozsa, An introduction to measurement based quantum computation, (2005) arXiv:quant-ph/0508124