Optimizing the walk coin in the quantum random walk search algorithm

Abstract

This paper examines quantum random walk search algorithm with walk coin constructed by generalized Householder reflection and additional phase shift factor. The results from numerical simulations with neural network show that, with such a construction of the walk coin, the algorithm is more robust to inaccuracies in the specific values of its parameters, as long as it is possible to control the phase difference between the phase shift factor and the phase involved in the Householder reflection. This paper explicitly shows how achieving a properly designed phase difference would make quantum random walk search on a hypercube more robust for coin register consisting of one, two and three qubits.