Photons walking the line: a quantum walk with adjustable coin operations.

We present the first robust implementation of a coined quantum walk over five steps using only passive optical elements. By employing a fiber network loop we keep the amount of required resources constant as the walker's position Hilbert space is increased. We observed a non-Gaussian distribution of the walker's final position, thus characterizing a faster spread of the photon wave packet in comparison to the classical random walk. The walk is realized for many different coin settings and initial states, opening the way for the implementation of a quantum-walk-based search algorithm.

[1]  Andris Ambainis,et al.  Quantum to classical transition for random walks. , 2003, Physical review letters.

[2]  Roberto Morandotti,et al.  Realization of quantum walks with negligible decoherence in waveguide lattices. , 2007, Physical review letters.

[3]  J Glueckert,et al.  Quantum walk of a trapped ion in phase space. , 2009, Physical review letters.

[4]  Dirk Bouwmeester,et al.  Optical Galton board , 1999 .

[5]  I. Jex,et al.  Localization and diffusion in Ising-type quantum networks , 2001, quant-ph/0103169.

[6]  S. Barnett,et al.  Measuring the orbital angular momentum of a single photon. , 2002, Physical review letters.

[7]  J. D. Franson,et al.  Photon-number resolution using time-multiplexed single-photon detectors , 2003, quant-ph/0305193.

[8]  Mark Hillery,et al.  Quantum walks based on an interferometric analogy , 2003 .

[9]  I. Jex,et al.  Optimized quantum random-walk search algorithms on the hypercube , 2008, 0805.4347.

[10]  Stephen P. Walborn,et al.  Quantum random walks and wave-packet reshaping at the single-photon level , 2008 .

[11]  P. Anderson Absence of Diffusion in Certain Random Lattices , 1958 .

[12]  Konrad Banaszek,et al.  Photon counting with a loop detector. , 2003, Optics letters.

[13]  Benjamin M. Zwickl,et al.  Experimental realization of a quantum quincunx by use of linear optical elements , 2005 .

[14]  Andrew M. Childs,et al.  Universal computation by quantum walk. , 2008, Physical review letters.

[15]  K. Birgitta Whaley,et al.  Quantum random-walk search algorithm , 2002, quant-ph/0210064.

[16]  S. Chandrasekhar Stochastic problems in Physics and Astronomy , 1943 .

[17]  Reck,et al.  Experimental realization of any discrete unitary operator. , 1994, Physical review letters.

[18]  I Jex,et al.  Recurrence and Pólya number of quantum walks. , 2007, Physical review letters.

[19]  Aharonov,et al.  Quantum random walks. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[20]  Dieter Meschede,et al.  Quantum Walk in Position Space with Single Optically Trapped Atoms , 2009, Science.

[21]  Guang-Can Guo,et al.  Demonstration of one-dimensional quantum random walks using orbital angular momentum of photons , 2007 .

[22]  L. Bachelier,et al.  Théorie de la spéculation , 1900 .

[23]  P. Knight,et al.  Quantum walk on the line as an interference phenomenon , 2003, quant-ph/0304201.

[24]  Christine Silberhorn,et al.  Fiber-assisted detection with photon number resolution. , 2003, Optics letters.

[25]  S. Lloyd,et al.  Environment-assisted quantum walks in photosynthetic energy transfer. , 2008, The Journal of chemical physics.

[26]  J. D. Franson,et al.  Cyclical Quantum Memory for Photonic Qubits , 2002 .