Simulation of quantum random walks using the interference of a classical field

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 69, Issue 1, 2004, Pages 123101-123107

  Jeong, H ^a   Paternostro, M ^a   Kim, M S ^a  

^a QUEEN'S UNIVERSITY BELFAST   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BROWNIAN MOVEMENT; COMPUTER SIMULATION; CONTINUUM MECHANICS; DEGREES OF FREEDOM (MECHANICS); ELECTROMAGNETIC WAVE INTERFERENCE; INTERFEROMETERS; LIGHT POLARIZATION; MATHEMATICAL MODELS; PHASE SHIFTERS; QUANTUM THEORY;

GAUSSIAN DISTRIBUTIONS; QUANTUM RANDOM WALKS;

QUANTUM OPTICS;

EID: 8644239853     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
2. U. Schöning, Proceedings of the 40th Annual Symposium on Foundations of Computer Science, New York, 1999 (unpublished); M. Jerrum, A. Sinclair, and E. Vigoda, Proceedings of the 33rd ACM Symposium on Theory of Computing, 2001 (unpublished).
3. U. Schöning, Proceedings of the 40th Annual Symposium on Foundations of Computer Science, New York, 1999 (unpublished); M. Jerrum, A. Sinclair, and E. Vigoda, Proceedings of the 33rd ACM Symposium on Theory of Computing, 2001 (unpublished).
4. R. A. Dana and M. Jeanblanc, Financial Markets in Continuous Time (Springer, Berlin, 2002).
5. A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, and J. Watrous, in Proceedings of the 33rd STOC (Association for Comp. Machinery, New York, 2001); D. Aharanov, A. Ambainis, J. Kempe, U. Vazirani, ibid.; J. Kempe, e-print quant-ph/0205083.
6. A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, and J. Watrous, in Proceedings of the 33rd STOC (Association for Comp. Machinery, New York, 2001); D. Aharanov, A. Ambainis, J. Kempe, U. Vazirani, ibid.; J. Kempe, e-print quant-ph/0205083.
7. A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, and J. Watrous, in Proceedings of the 33rd STOC (Association for Comp. Machinery, New York, 2001); D. Aharanov, A. Ambainis, J. Kempe, U. Vazirani, ibid.; J. Kempe, e-print quant-ph/0205083.
8. J. Kempe, Contemp. Physics 44, 307 (2003).
9. B.C. Travaglione and G.J. Milburn, Phys. Rev. A 65, 032310 (2002); W. Dür, R. Raussendorf, V.M. Kendon, and H.-J. Briegel, ibid 66, 052319 (2002); B.C. Sanders, S.D. Bartlett, B. Tregenna, and P.L. Knight, ibid. 67, 042305 (2003).
10. B.C. Travaglione and G.J. Milburn, Phys. Rev. A 65, 032310 (2002); W. Dür, R. Raussendorf, V.M. Kendon, and H.-J. Briegel, ibid 66, 052319 (2002); B.C. Sanders, S.D. Bartlett, B. Tregenna, and P.L. Knight, ibid. 67, 042305 (2003).
11. B.C. Travaglione and G.J. Milburn, Phys. Rev. A 65, 032310 (2002); W. Dür, R. Raussendorf, V.M. Kendon, and H.-J. Briegel, ibid 66, 052319 (2002); B.C. Sanders, S.D. Bartlett, B. Tregenna, and P.L. Knight, ibid. 67, 042305 (2003).
12. Z. Zhao, J. Du, H. Li, T. Yang, Z.-B. Chen, and J.-W. Pan, e-print quant-ph/0212149.
13. M. Hillery, J. Bergou, and E. Feldman, Phys. Rev. A 68, 032314 (2003).
14. A.M. Childs, E. Deotto, E. Farhi, J. Goldstone, S. Gutmann, and A.J. Landahl, Phys. Rev. A 66, 032314 (2002); N. Shenvi, J. Kempe, and K.B. Whaley, quant-ph/0210064.
15. A.M. Childs, E. Deotto, E. Farhi, J. Goldstone, S. Gutmann, and A.J. Landahl, Phys. Rev. A 66, 032314 (2002); N. Shenvi, J. Kempe, and K.B. Whaley, quant-ph/0210064.
16. V. Kendon and B. Tregenna, Phys. Rev. A 67, 042315 (2003); T.A. Brun, H.A. Cateret, and A. Ambainis, ibid.67, 032304 (2003).
17. V. Kendon and B. Tregenna, Phys. Rev. A 67, 042315 (2003); T.A. Brun, H.A. Cateret, and A. Ambainis, ibid.67, 032304 (2003).
18. Note that classical random walks can be easily obtained by removing all the phase shifters. In this case, indeed, there can be no destructive interference that makes the quantum random walk different from its classical counterpart.
19. A. Stefanov, H. Zbinden, N. Gisin, and A. Suarez, Phys. Rev. Lett. 88, 120404 (2002).
20. M.S. Kim, W. Son, V. Buzek, and P.L. Knight, Phys. Rev. A 65, 032323 (2002).
21. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).
22. P. Törmä, I. Jex, and W.P. Schleich, Phys. Rev. A 65, 052110 (2002).
23. F. Haake, Quantum Signature of Chaos (Springer-Verlag, Berlin, 1992).
24. D. Bouwmeester, I. Marzoli, G. Karman, W.P. Schleich, and J.P. Woerdman, Phys. Rev. A 61, 013410 (2000).
25. P.L. Knight, E. Roldan, and J.E. Sipe, Phys. Rev. A 68, 020301(R) (2003).
26. More precisely, while the number of beam splitters grows as N, the required AOMs and phase shifters increases as 2N. However, in the spirit of the proposal shown in Fig. 1, we can consider basic building blocks made by a beam splitter, two phase shifters, and two AOMs (as the one boxed in Fig. 3). This clarifies that, in this case, the number of building blocks grows linearly with N.