Download A quantum walk based search algorithm, and its optical realisation

A quantum walk based search algorithm,
and its optical realisation
Aurél Gábris
FJFI, Czech Technical University in Prague
[email protected]
Abstract
Quantum walks are quantum mechanical generalisations of classical random walks. Quantum walks
are considered as a promising tool for the construction of efficient quantum algorithms: a key challenge for
the practical use of a future quantum computer. Among other applications, the quantum walk paradigm
has been successfully used for designing quantum search algorithms.
I will begin my talk with an introduction to quantum walks on general graphs, and discuss a particular quantum walk search algorithm by Shenvi, Kempe and Whaley (SKW) [1]. Although the SKW
algorithm’s complexity scales with the size of the search space identically to the Grover’s search, there
are some subtle differences, which will also be discussed. Following, I will present an optical network that
can be used for the realization of the SKW quantum walk search algorithm, providing a good example
for a spatial search. I will briefly recall our results on the analysis of the impact of photon loss and phase
imperfections, which are typical sources of errors in this particular physical system [2].
References
[1] N. Shenvi, J. Kempe, and K. B. Whaley, Phys. Rev. A 67, 052307 (2003).
[2] A. Gábris, T. Kiss, and I. Jex, Phys. Rev. A 76, 062315 (2007).