Robustness of quantum random walk search with multi-phase matching

Abstract

In our previous works, we have studied quantum random walk search algorithm on hypercube, with traversing coin constructed by using generalized Householder reflection and a phase multiplier. When the same phases are used each iteration, the algorithm is robust (stable against errors in the phases) if a certain connection between the phases in the traversing coin is preserved, otherwise small errors lead to poor algorithm performance. Here, we investigate how the robustness changes if different phases are used, depending on the current iteration number. We numerically study six different examples with different phase sequences. We show that usage of a particular sequence of phases can make the algorithm more robust even if there is no preserved connection between the phases in the traversing coin.