Search Via quantum walks with intermediate measurements

TL;DR

This paper presents a modified quantum search algorithm with intermediate measurements, analyzing how measurement timing affects performance and correlations, and demonstrating potential improvements over classical and other quantum algorithms.

Contribution

It introduces a new variant of Tulsi's quantum search with intermediate control measurements and analyzes its performance and correlations for different measurement intervals.

Findings

Performance improves with optimized measurement intervals

Algorithm can achieve classical order $O(N)$ with frequent measurements

Measurements influence correlations and success probabilities

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.