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This paper examines the stability of the quantum random walk searchalgorithm, when the walk coin is constructed by generalized Householderreflection and additional phase shift, against inaccuracies in the phases usedto construct the coin. The optimization of the algorithm is done by numericalmethods - Monte Carlo, neural networks, and supervised machine learning. Theresults of numerical simulations show that, with such a construction of theHouseholder reflection, the algorithm is more stable to inaccuracies in thespecific values of these phases, as long as it is possible to control the phasedifference between the phase shift and the phase involved in the Householderreflection. This paper explicitly shows as an example, how achieving a properlydesigned phase difference would make quantum random walk search on a hypercubemore stable for coin register consisting of one, two, and three qubits.

Optimizing the walk coin in the quantum random walk search algorithm through machine learning