Quantum walks with entangled coins

New Journal of Physics

Volumn 7, Issue , 2005, Pages

  Venegas Andraca, S E ^a   Ball, J L ^a   Burnett, K ^a   Bose, S ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DEGREES OF ENTANGLEMENT; QUANTUM WALKS; SHIFT OPERATORS; TWO-DIMENSIONAL GRAPHS;

GRAPH THEORY; NUMERICAL ANALYSIS; PROBABILITY DISTRIBUTIONS;

QUANTUM THEORY;

EID: 26844565191     PISSN: 13672630     EISSN: 13672630     Source Type: Journal    
DOI: 10.1088/1367-2630/7/1/221     Document Type: Review

References (45)

1. Motwani R and Raghavan P 1995 Randomized Algorithms (Cambridge: Cambridge University Press)
2. Hofmeister T, Schöning U, Schuler R and Watanabe O 2002 A probabilistic 3-SAT algorithm further improved 19th Symp. Theoret. Aspects of Comput. Sci. (Berlin: Springer) pp 192-202
3. Farhi E and Gutmann S 1998 Phys. Rev. A 58 915-28
4. Childs A, Farhi E and Gutmann S 2001 Quantum Inform. Process. 1 35
5. Moore C and Russell A 2002 Quantum walks on the hypercube Proc. 6th Int. Workshop on Randomization and Approximation Techniques in Computer Science (Lecture Notes in Computer Science vol 2483 (Berlin: Springer) pp 164-78
6. Gerhardt H and Watrous J 2003 Continuous-time quantum walks on the symmetric group Proc. 7th Int. Workshop on Randomization and Approximation Techniques in Computer Science (Berlin: Springer) pp 290-301
7. Ahmadi A, Belk R, Tamon C and Wendler C 2003 Quantum Inform Comput. 3 611-8
8. Fedichkin L, Solevon D and Tamon C 2004 Mixing and decoherence in continuous-time quantum walks on cycles Preprint quant-ph/0509163
9. Aharonov Y, Davidovich L and Zagury N 1993 Phys. Rev. A 48 1687-90
10. Meyer D A 1996 J. Stat. Phys. 85 551-74
11. Nayak A and Vishwanath A 2000 Preprint quant-ph/0010117
12. Aharonov D, Ambainis A, Kempe J and Vazirani U 2001 Quantum walks on graphs Proc. 33th ACM Symp. on The Theory of Computing (New York) pp 50-59
13. Brun T A, Carteret H A and Ambainis A 2003 Phys. Rev. Lett. 91 130602
14. Jeong H, Paternostro M and Kim M S 2004 Phys. Rev. A 69 012310
15. Knight P L, Roldán E and Sipe J E 2004 J. Mod. Opt. 51 1761-77
16. Childs A M, Cleve R, Deotto E, Farhi E, Gutmann S and Spielman D 2003 Exponential algorithmic speedup by quantum walk Proc. 35th ACM Symp. on The Theory of Computing (New York) pp 59-68
17. Ambainis A, Bach E, Nayak A, Vishwanath A and Watrous J 2001 One-dimensional quantum walks Proc. 33rd STOC-ACM (New York) pp 60-9
18. Kempe J 2003 Discrete quantum walks hit exponentially faster Proc. 7th Int. Workshop on Randomization and Approximation Techniques in Computer Science (Berlin: Springer) pp 354-69
19. Shenvi N, Kempe J and Whaley K B 2003 Phys. Rev. A 67 052307
20. Ambainis A 2004 Quantum walk algorithm for element distinctness Proc. 45th Annual IEEE Symp. on Foundations of Computer Science (Piscataway, NJ: IEEE) pp 22-31
21. Kempe J 2003 Contemp. Phys. 44 307-27
22. Ambainis A 2003 Quantum walks and their algorithmic applications Int. J. Quantum Inform. 1 507-18
23. Brun T A, Carteret H A and Ambainis A 2003 Phys. Rev. A 67 052317
24. Tregenna B, Flanagan W, Maile R and Kendon V 2003 New J. Phys. 5 83
25. Ambainis A, Kempe J and Rivosh A 2005 Coins make quantum walks faster Proc. 16th ACM-SIAM SODA pp 1099-1108 (Preprint quant-ph/0402107)
26. Kendon V and Tregenna B 2003 Phys. Rev. A 67 042315
27. Kendon V and Tregenna B 2003 Decoherence in discrete quantum walks Selected Lectures from DICE 2002 Lecture Notes in Physics vol 633)(Berlin: Springer) pp 253-67
28. Brun T A, Carteret H A and Ambainis A 2003 Phys. Rev. A 67 032304
29. MacKay T D, Bartlett S D, Stephenson L T and Sanders B C 2002 Quantum walks in higher dimensions J. Phys. A Math. Gen. 35 2745-53
30. Du J, Li H, Xu X, Shi M, Wu J, Zhou X and Han R 2003 Phys. Rev. A 67 042316
31. Omar Y, Paunković N, Sheridan L and Bose S 2004 Preprint quant-ph/0411065
32. Carneiro I, Loo M, Xu X, Girerd M, Kendon V and Knight P 2005 New J. Phys. 7 156
33. Endrejat J and Buttner H 2005 Preprint quant-ph/0507184
34. Abal G, Siri R, Romanelli A and Donangelo R 2005 Preprint quant-ph/0507264
35. Sanders B C, Bartlett S D, Tregenna B and Knight P L 2003 Phys. Rev. A 67 042305
36. Travaglione B C and Milburn G J 2002 Phys. Rev. A 65 032310
37. Rowe M A, Kielpinski D, Meyer V, Sacket C A, Itano W M, Monroe C and Wineland D J 2001 Nature 409 791-4
38. Plenio M B, Huelga S F, Beige A and Knight P L 1999 Phys. Rev. A 59 2468-75
39. Grimmett G and Welsh D 1991 Probability: An Introduction (Oxford: Oxford University Press)
40. Bennett C H, Bernstein H J, Popescu S and Schumacher B 1996 Phys. Rev. A 53 2046
41. Bach E, Coppersmith S, Paz Goldshen M, Joynt R and Watrous J 2004 J. Comput. Syst. Sci. 69 562-92
42. Yamasaki T, Kobayashi H and Imai H 2003 Phys. Rev. A 68 012302
43. Schöning U 1999 A probabilistic algorithm for k-SAT and constraint satisfaction problems Proc. IEEE Symp. on Foundations of Computer Science pp 410-14
44. Inui N and Konno N 2005 Localization of multi-state quantum walk in one dimension Physica A 353 133-44
45. Roldán E and Soriano J C 2005 Preprint quant-ph/0503069