Optimized quantum random-walk search algorithms on the hypercube

Potocek, V., Gábris, A., Kiss, T. and Jex, I. (2009) Optimized quantum random-walk search algorithms on the hypercube. Physical Review A: Atomic, Molecular and Optical Physics, 79(1), 012325. (doi: 10.1103/PhysRevA.79.012325)

Abstract

Shenvi, Kempe, and Whaley’s quantum random-walk search (SKW) algorithm [Phys. Rev. A 67, 052307 (2003)] is known to require O(N−−√) number of oracle queries to find the marked element, where N is the size of the search space. The overall time complexity of the SKW algorithm differs from the best achievable on a quantum computer only by a constant factor. We present improvements to the SKW algorithm which yield a significant increase in success probability, and an improvement on query complexity such that the theoretical limit of a search algorithm succeeding with probability close to one is reached. We point out which improvement can be applied if there is more than one marked element to find.

• Item Type: Articles
• Status: Published
• Refereed: No
• Glasgow Author(s) Enlighten ID: Potocek, Dr Vaclav
• Authors: Potocek, V., Gábris, A., Kiss, T., and Jex, I.
• Subjects: Q Science > QC Physics
• College/School: College of Science and Engineering > School of Physics and Astronomy
• Journal Name: Physical Review A: Atomic, Molecular and Optical Physics
• Journal Abbr.: Phys. Rev. A
• Publisher: American Physical Society
• ISSN: 1050-2947
• ISSN (Online): 1094-1622

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