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In this work we study the robustness of two modifications of quantum randomwalk search algorithm on hypercube. In the first previously suggestedmodification, on each even iteration only quantum walk is applied. And in thesecond, the closest neighbors of the solution are measured classically. In ourapproach the traversing coin is constructed by both generalized Householderreflection and an additional phase multiplier and we investigate the stabilityof the algorithm to deviations in those phases. We have shown that theunmodified algorithm becomes more robust when a certain relation between thosephases is preserved. The first modification we study here does not lead to anychange in the robustness of quantum random walk search algorithm. However, whena measurement of the first and second neighbors is included, there are somedifferences. The most important one, in view of our study of the robustness, isan increase in the stability of the algorithm, especially for large coindimensions.

Robustness of Quantum Random Walk Search Algorithm in Hypercube when only first or both first and second neighbors are measured