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Phys. Rev. A 69, 010302(R) (2004) [4 pages]

Efficient optical implementation of the Bernstein-Vazirani algorithm

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P. Londero1, C. Dorrer2, M. Anderson3, S. Wallentowitz4, K. Banaszek1, and I. A. Walmsley1,*
1Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, United Kingdom
2Bell Laboratories, Lucent Technologies, 101 Crawfords Corner Road, Holmdel, New Jersey 07733, USA
3Physics Department, San Diego State University, 5500 Campanile Drive, San Diego, California 92182-1233, USA
4Fachbereich Physik, Universität Rostock, Universitätsplatz 3, D-18051 Rostock, Germany

Received 24 January 2003; published 9 January 2004

We implement the Bernstein-Vazirani algorithm on a 15-bit register encoding 215 elements using optics. The algorithm provides a polynomial speed up for oracle queries. The apparatus is physically efficient in that its size (i.e., space-time volume) scales linearly with the size (i.e., number of digits) of the register. We demonstrate also that the algorithm may be performed not only without entanglement, but also with a computational basis that does not consist of orthogonal states, and that this coding is the source of the efficiency of the algorithm.

© 2004 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.69.010302
DOI:
10.1103/PhysRevA.69.010302
PACS:
03.67.Lx, 42.50.-p

*Electronic address: walmsley@physics.ox.ac.uk

 
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