Quantum fast Fourier transform and quantum computation by linear optics

Journal of the Optical Society of America B: Optical Physics

Volumn 24, Issue 2, 2007, Pages 231-240

  Barak, Ronen ^a   Ben Aryeh, Yacob ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ESTIMATION; FAST FOURIER TRANSFORMS; OPTICAL BEAM SPLITTERS; OPTICAL SYSTEMS; QUANTUM COMPUTERS;

COOLEY-TUKEY ALGORITHM; LINEAR OPTICS; QUANTUM FAST FOURIER TRANSFORM;

QUANTUM OPTICS;

EID: 33947260994     PISSN: 07403224     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAB.24.000231     Document Type: Article

References (33)

1. A. Ekert, "Quantum interferometers as quantum computers," Phys. Scr. 1, 218-222 (1998).
2. M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, "Experimental realization of any discrete unitary operator," Phys. Rev. Lett. 73, 58-61 (1994).
3. D. Bouwmeester, J. C. Howell, and A. Lamas-Linares, "Quantum information science using photons," in Fundamentals of Quantum Information: Quantum Computation, Communication, Decoherence, and All That, D. Heiss, ed. (Springer, 2002), pp. 149-197.
4. N. J. Cerf, C. Adami, and P. G. Kwiat, "Optical simulation of quantum logic," Phys. Rev. A 57, R1477-R1480 (1998).
5. G. M. D'Ariano, C. Macchiavello, and L. Maccone, "Quantum computations with polarized photons," Fortschr. Phys. 48, 573-577 (2000).
6. J. C. Howell and J. A. Yeazell, "Quantum computation through entangling single photons in multipath interferometers," Phys. Rev. Lett. 85, 198-201 (2000).
7. S. Takeuchi, "A simple quantum computer: experimental realization of quantum computation algorithms with linear optics," Electron. Commun. Jpn. Part 3 84, 52-60 (2001).
8. S. Takeuchi, "Analysis of errors in linear-optics quantum computational," Phys. Rev. A 61, 052302 (2000).
9. H. F. Hofmann and S. Takeuchi, "Quantum phase gate for photonic qubits using only beam splitters and postselection," Phys. Rev. A 66, 024308/1-3 (2002).
10. T. C. Ralph, A. G. White, W. J. Munro, and G. J. Milburn, "Simple scheme for efficient linear optics quantum gates," Phys. Rev. A 65, 012314 (2001).
11. G. J. Milburn, T. Ralph, A. White, E. Knill, and R. Laflamme, "Efficient linear optics quantum computation," Quantum Inf. Comput. 1, 13-19 (2001).
12. E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).
13. J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).
14. N. Yoran and B. Reznik, "Deterministic linear optics quantum computation with single photon qubits," Phys. Rev. Lett. 91, 037903/1-4 (2003).
15. J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Comput. 19, 297-301 (1965).
16. E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, 1975).
17. H. J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms (Springer, 1981).
18. J. S. Walker, Fast Fourier Transforms, (CRS Press, 1996).
19. P. Törmä, I. Jex, and S. Stenholm, "Beam splitter realizations of totally symmetric mode couplers," J. Mod. Opt. 43, 245-251 (1996).
20. M. Zukowski, A. Zeilinger, and M. A. Horne, "Realizable higher-dimensional two-particle entanglements via multiport beam splitters," Phys. Rev. A 55, 2564-2579 (1997).
21. K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, and M. Zukowski, "Nonclassical statistics at multiport beam splitters," Appl. Phys. B 60, S111-S117 (1995).
22. P. W. Shor, "Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer," SIAM J. Comput. 26, 1484-1509 (1997).
23. A. Ekert and R. Jozsa, "Quantum computation and Shor's factoring algorithm," Rev. Mod. Phys. 68, 733-753 (1996).
24. A. Ekert, P. Hayden, H. Inamori, and D. K. L. Oi, "What is quantum computation?" Int. J. Mod. Phys. A 16, 3335-3363 (2001).
25. R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca, "Quantum algorithms revisited," Proc. R. Soc. London Ser. A 454, 339-354 (1998).
26. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2000).
27. A. E. Siegman, "Fiber Fourier optics," Opt. Lett. 26, 1215-1217 (2001).
28. U. Leonhardt, Measuring the Quantum State of Light (Cambridge U. Press, 1997).
29. G. D. Bergland, "A guided tour of the fast Fourier transforms," IEEE Spectrum 6, 41-52 (1969).
30. N. G. Walker, "Quantum theory of multiport optical homodyning," J. Mod. Opt. 34, 15-60 (1987).
31. G. Benenti, G. Casati, G. Strini, Principles of Quantum Computation and Information, Volume I: Basic Concepts (World Scientific, 2004).
32. V. Vedral, "The role of relative entropy in quantum information theory," Rev. Mod. Phys. 74, 197-234 (2002).
33. G. P. Berman, G. D. Doolen, R. Mainieri, and V. I. Tsifrinovich, Introduction to Quantum Computers (World Scientific, 1998).