Title: Optimizing a quantum random walk search algorithm
Speaker: Václav Potoček, FJFI, CTU Prague
E-mail: potocvac@fjfi.cvut.cz
Abstract:
Unordered database searching is one of the most important algorithmic tasks
where quantum algorithms were shown to be able to surpass the theoretical
bounds of any classical algorithm. Similarly, random walks are a powerful and
widely used algorithmic concept, quantum algorithmic analogue of which shows
many interesting properties. Combining these two premises, a quantum random
walk search algorithm has been presented [1]. It has also been proven to reach
approximately the theoretical bounds valid for any possible quantum algorithm
[2], however, there are some significant limitations.
In the beginning of the talk, I will emphasize the differences from the nearly
optimal Grover's quantum search algorithm [3]. I will describe the source of
the most obvious difference in the maximal success probability of the two
algorithms. In the main part, I will discuss several ways of modifying the
random walk algorithm we propose in order to avoid this difference. Along
these modifications, further similarities with the Grover's algorithm arise,
moving the original algorithm significantly closer to the optimal theoretical
bound.
[1] N. Shenvi, J. Kempe, and K. B. Whaley, Phys. Rev. A 67, 052307 (2003)
[2] M. Boyer, G. Brassard, P. Hoeyer, A. Tapp, Tight bounds on quantum
searching, arXiv:quant-ph/9605034v1 (1996)
[3] L. Grover, in Proceedings, 28th Annual ACM Symposium on the Theory of
Computing (STOC), p. 212 (1996)