Effects of systematic phase errors on optimized quantum random-walk search algorithm

TL;DR

This paper investigates how systematic phase errors impact the success rate and efficiency of an optimized quantum random-walk search algorithm, providing models and analysis of its robustness compared to Grover's algorithm.

Contribution

It establishes a geometric model for the algorithm with phase errors and analyzes its performance, highlighting its greater robustness over Grover's algorithm.

Findings

Maximum success rate with phase errors is quantified.

Number of iterations needed is determined under phase errors.

The algorithm demonstrates higher robustness than Grover's algorithm.

Abstract

This paper researches how the systematic errors in phase inversions affect the success rate and the number of iterations in optimized quantum random-walk search algorithm. Through geometric description of this algorithm, the model of the algorithm with phase errors is established and the relationship between the success rate of the algorithm, the database size, the number of iterations and the phase error is depicted. For a given sized database, we give both the maximum success rate of the algorithm and the required number of iterations when the algorithm is in the presence of phase errors. Through analysis and numerical simulations, it shows that optimized quantum random-walk search algorithm is more robust than Grover's algorithm.