Quantum walks with history dependence

Journal of Physics A: Mathematical and General

Volumn 37, Issue 30, 2004, Pages 7581-7591

  Flitney, A P ^a   Abbott, D ^b   Johnson, N F ^b  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3543009603     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/30/013     Document Type: Article

References (43)

1. Papadimiriou C 1994 Computational Complexity (Reading, MA: Addison-Wesley)
2. Motwani R and Raghavan P 1995 Randomized Algorithms (Cambridge: Cambridge University Press)
3. Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
4. Lee C F and Johnson N F 2002 Let the quantum games begin Phys. World (October) 25
5. Farhi E and Gutmann S 1998 Quantum computation and decision trees Phys. Rev. A 58 915-28
6. Childs A, Farhi E and Gutmann S 2002 An example of the difference between quantum and classical random walks Quantum Inf. Process. 1 35-43
7. Aharonov Y, Davidovich L and Zagury N 1993 Quantum random walks Phys. Rev. A 48 1687-90
8. Meyer D A 1996 From quantum cellular automata to quantum lattice gases J. Stat. Phys. 85 551-74
9. Watrous J 2001 Quantum simulations of classical random walks and undirected graph connectivity J. Comput. Syst. Sci. 62 376-91
10. Aharonov D, Ambainis A, Kempe J and Varzirani U 2001 Quantum random walks on graphs Proc. 33rd ACM Symp. on Theory of Computing (STOC 2001) (New York: Soc. for Comp. Machinery) pp 50-60
11. Ambainis A, Bach E, Nayak A, Viswanath A and Watrous J 2001 One-dimensional quantum walks Proc. 33rd ACM Symp. on Theory of Computing (STOC 2001) (New York: Soc. for Comp. Machinery) pp 60-72
12. Meyer D A and Blumer H 2001 Parrondo games as lattice gas automata J. Stat. Phys. 107 225-39
13. Nayak A and Vishwanath A 2000 Quantum walk on a line Preprint quant-ph/0010117
14. Travaglione B C and Milburn G J 2001 Implementing the quantum random walk Phys. Rev. A 65 032310
15. Childs A M, Cleve R, Deotto E, Farhi E, Gutmann S and Spielman D A 2002 Exponential algorithmic speedup by quantum walk Proc. 35th ACM Symp. on Theory of Computing (STOC 2003) (New York: Soc. for Comp. Machinery) pp 59-68
16. Shenvi N, Kempe J and Whaley K B 2003 A quantum random walk search algorithm Phys. Rev. A 67 052307
17. Dür W, Raussendorf R, Kendon V M and Briegel H-J 2002 Quantum walks in optical lattices Phys. Rev. A 66 052319
18. Sanders B C, Bartlett S D, Tregenna B and Knight P L 2003 Quantum quincunx in cavity quantum electrodynamics Phys. Rev. A 67 042305
19. Du J, Li H, Xu X, Shi M, Wu J, Zhou X and Han R 2003 Experimental implementation of a quantum random walk algorithm Phys. Rev. A 67 042316
20. Kempe J 2003 Quantum random walks: an introductory overview Contemporary Physics 44 307-27
21. Parrondo J M R 1996 EEC HC&M Network on Complexity and Chaos (ERBCHRX-CT940546) ISI (Torino, Italy)
22. Harmer G P, Abbott D, Taylor P G and Parrondo J M R 1999 Parrondo's paradoxical games and discrete Brownian ratchets Proc. 2nd Int. Conf. on Unsolved Problems of Noise and Fluctuations (UPoN '99) vol 511 ed D Abbott and L B Kish (American Institute of Physics) pp 189-200
23. McClintock P V E 1999 Random fluctuations: unsolved problems of noise Nature 40123-5
24. Harmer G P and Abbott D 1999 Parrondo's games Stat. Sci. 14 206-13 Harmer G P and Abbott D 1999 Losing strategies can win by Parrondo's paradox Nature 402 86
25. Harmer G P and Abbott D 1999 Parrondo's games Stat. Sci. 14 206-13 Harmer G P and Abbott D 1999 Losing strategies can win by Parrondo's paradox Nature 402 86
26. Parrondo J M R, Harmer G P and Abbott D 2000 New paradoxical games based on Brownian ratchets Phys. Rev. Lett. 85 5226-9
27. Toral R 2001 Cooperative Parrondo's games Fluct. Noise Lett. 1 L7-12
28. Feynman R P, Leighton P B and Sands M 1963 Feynman Lectures on Physics vol 1 (Reading, MA: Addison-Wesley) chapter 46
29. Harmer G P, Abbott D, Taylor P G and Parrondo J M R 2001 Brownian ratchets and Parrondo's games Chaos 11 705-14
30. Allison A and Abbott D 2002 The physical basis of Parrondo's games Fluct. Noise Lett. 2 L327-41
31. Lee Y, Allison A, Abbott D and Stanley H E 2003 Minimal Brownian ratchet: an exactly solvable model Phys. Rev. Lett. 91 220601
32. Moraal H 2000 Counter intuitive behavior in games based on spin models J. Phys. A: Math. Gen. 33 L203-6
33. Davies P C W 2001 The First Steps of Life in the Universe Lecture in honor of Abdus Salam, Proc. 6th Trieste Conf. on Chemical Evolution (Trieste, Italy) ed J Chela-Flores, T Owen and F Raulin (Dordrecht: Kluwer) pp 13-22
34. Klarreich E 2001 Playing both sides The Sciences 41 25-34
35. Ng J and Abbott D (in press) Introduction to quantum games and a quantum Parrondo game Ann. Int. Soc. on Dynamic Games ed A Nowac (Boston: Birkhauser)
36. Flitney A P, Ng J and Abbott D 2002 Quantum Parrondo's games Physica A 314 35-42
37. Lee C F, Johnson N F, Rodriguez F and Quiroga L 2002 Quantum coherence, correlated noise and Parrondo games Fluct. Noise Lett. 2 L293-8
38. Lee C F and Johnson N F 2002 Exploiting randomness in quantum information processing Phys. Rev. Lett. A 301 343-9
39. Harmer G P and Abbott D 2002 A review of Parrondo's paradox Fluct. Noise Lett. 2 R71-107
40. Flitney A P and Abbott D 2003 Quantum models of Parrondo's games Physica A 324 152-6
41. Kay R and Johnson N F 2002 Winning combinations of history dependent games Preprint cond-mat/0207386
42. Brun T A, Carteret H A and Ambainis A 2003 Quantum walks driven by many coins Phys. Rev. A 67 052317
43. Brun T A, Carteret H A and Ambainis A 2003 Quantum random walks with decoherent coins Phys. Rev. A 67 032304