Alternative Coins for Quantum Random Walk Search Optimized for a Hypercube

Abstract

The present paper is focused on non-uniform quantum coins for the quantum random walk search algorithm. This is an alternative to the modification of the shift operator, which divides the search space into two parts. This method changes the quantum coins, while the shift operator remains unchanged and sustains the hypercube topology. The results discussed in this paper are obtained by both theoretical calculations and numerical simulations.