Bosonic and Fermionic Quantum Walk

  • Linda SansoniEmail author
Part of the Springer Theses book series (Springer Theses)


As seen in the previous chapter, single-particle quantum walks yield an exponential computational gain with respect to classical random walks. Here we address the quantum walk of a large number of indistinguishable particles: it can provide an additional computational power that scales exponentially with the employed resources.


Entangle State Beam Splitter Stable Match Quantum Walk Optical Implementation 
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  1. 1.
    J.K. Gamble, M. Friesen, D. Zhou, R. Joynt, S.N. Coppersmith, Two-particle quantum walks applied to the graph isomorphism problem. Phys. Rev. A 81, 052313 (2010)ADSCrossRefGoogle Scholar
  2. 2.
    A. Peruzzo, M. Lobino, J.C.F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Worhoff, Y. Bromberg, Y. Silberberg, M.G. Thompson, J.L. O’Brien, Quantum walks of correlated photons. Science 329, 1500 (2010)Google Scholar
  3. 3.
    J.O. Owens, M.A. Broome, D.N. Biggerstaff, M.E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G.D. Marshall, J. Twamley, M.J. Withford, A.G. White, Two-photon quantum walks in an elliptical direct-write waveguide array. New J. Phys. 13, 075003 (2011)ADSCrossRefGoogle Scholar
  4. 4.
    Y. Omar, N. Paunković, L.S.S. Bose, Quantum walk on a line with two entangled particles. Phys. Rev. A 74, 042304 (2006)ADSCrossRefMathSciNetGoogle Scholar
  5. 5.
    P.K. Pathak, G.S. Agarwal, Quantum random walk of two photons in separable and entangled states. Phys. Rev. A 75, 032351 (2007)ADSCrossRefMathSciNetGoogle Scholar
  6. 6.
    H. Jeong, M. Paternostro, M.S. Kim, Simulation of quantum random walks using the interference of a classical field. Phys. Rev. A 69, 012310 (2004)ADSCrossRefGoogle Scholar
  7. 7.
    P.P. Rohde, A. Schreiber, M. Stefank, I. Jex, C. Silberhorn, Multi-walker discrete time quantum walks on arbitrary graphs, their properties and their photonic implementation. New J. Phys. 13, 013001 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    Y. Bromberg, Y. Lahini, R. Morandotti, Y. Silberberg, Quantum and classical correlations in waveguide lattices. Phys. Rev. Lett. 102, 253904 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    A. Schreiber, K.N. Cassemiro, V. Potocek, A. Gabris, P.J. Mosley, E. Andersson, I. Jex, C. Silberhorn, Photons walking the line: a quantum walk with adjustable coin operations. Phys. Rev. Lett. 104, 050502 (2010)Google Scholar
  10. 10.
    M.A. Broome, A. Fedrizzi, B.P. Lanyon, I. Kassal, A. Aspuru-Guzik, A.G. White, Discrete single-photon quantum walks with tunable decoherence. Phys. Rev. Lett. 104, 153602 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, R. Osellame, Two-particle bosonic-fermionic quantum walk via integrated photonics. Phys. Rev. Lett. 108, 010502 (2012)ADSCrossRefGoogle Scholar
  12. 12.
    A. Schreiber, K.N. Cassemiro, V. Potocek, A. Gabris, P.J. Mosley, I. Jex, C. Silberhorn, Decoherence and disorder in quantum walks: from ballistic spread to localization. Phys. Rev. Lett. 106, 180403 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    A. Schreiber, A. Gábris, P.P. Rohde, K. Laiho, M. Stefank, V. Potocek, C. Hamilton, I. Jex, C. Silberhorn, A 2D quantum walk simulation of two-particle dynamics. Science 336, 55 (2012)Google Scholar
  14. 14.
    A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F.D. Nicola, F. Sciarrino, P. Mataloni, Anderson localization of entangled photons in an integrated quantum walk. Nat. Photonics 7, 322 (2013)Google Scholar
  15. 15.
    R.R. Gattass, E. Mazur, Femtosecond laser micromachining in transparent materials. Nat. Photonics 2, 219 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    G. Della Valle, R. Osellame, P. Laporta, Micromachining of photonic devices by femtosecond laser pulses. J. Opt. A: Pure Appl. Opt. 11, 049801 (2009).Google Scholar
  17. 17.
    J.C.F. Matthews, M.G. Thompson, Quantum optics: an entangled walk of photons. News Views Nature 484, 47 (2012)ADSGoogle Scholar
  18. 18.
    P. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, New high-intensity source of polarization entangled photon pairs. Phys. Rev. Lett. 75, 4337 (1995)ADSCrossRefGoogle Scholar
  19. 19.
    F. Wilczek, Magnetic flux, angular momentum, and statistics. Phys. Rev. Lett. 48, 1144 (1982)ADSCrossRefMathSciNetGoogle Scholar
  20. 20.
    P. Anderson, Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492 (1958)ADSCrossRefGoogle Scholar
  21. 21.
    P. Torma, I. Jex, W.P. Schleich, Localization and diffusion in Ising-type quantum networks. Phys. Rev. A 65, 052110 (2002)ADSCrossRefGoogle Scholar
  22. 22.
    J.P. Keating, N. Linden, J.C.F. Matthews, A. Winter, Localization and its consequences for quantum walk algorithms and quantum communication. Phys. Rev. A 76, 012315 (2007)ADSCrossRefGoogle Scholar
  23. 23.
    Y. Yin, D.E. Katsanos, S.N. Evangelou, Quantum walks on a random environment. Phys. Rev. A 77, 022302 (2008)ADSCrossRefMathSciNetGoogle Scholar
  24. 24.
    M. Mohseni, P. Rebentrost, S. Lloyd, A. Aspuru-Guzik, Environment-assisted quantum walks in photosynthetic energy transfer. J. Chem. Phys. 129, 174106 (2008)ADSCrossRefGoogle Scholar
  25. 25.
    F. Caruso, N. Spagnolo, C. Vitelli, F. Sciarrino, M.B. Plenio, Simulation of noise-assisted transport via optical cavity networks. Phys. Rev. A 83, 013811 (2011)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of PaderbornPaderbornGermany

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