Search Via quantum walks with intermediate measurements

Abstract

A modification of Tulsi's quantum search algorithm with intermediate measurements of the control is presented. In order to analyze the effect of measurements in quantum searches, a different choice of the angular parameter is used. The study is performed for several values of time lapses between measurements, finding close relationships between probabilities and correlations (Mutual Information and Cumulative Correlation Measure). The order of this modified algorithm is estimated, showing that for some time lapses the performance is improved, and became of order $O(N)$ (classical brute force search) when the measurement is taken in every step. The results indicate a possible way to analyze improvements to other quantum algorithms using one, or more, control qubits.

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