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arXiv · 0805.4347

Optimized quantum random-walk search algorithms

V. Potocek·A. Gabris·T. Kiss·I. Jex
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Abstract

Shenvi, Kempe and Whaley's quantum random-walk search (SKW) algorithm [Phys. Rev. A 67, 052307 (2003)] is known to require $O(\sqrt N)$ 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 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.

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V. Potocek, A. Gabris, T. Kiss, I. Jex. 2008-12-12. Optimized quantum random-walk search algorithms. https://doi.org/10.1103/physreva.79.012325

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