Quantum walk search for exceptional configurations

TL;DR

This paper compares quantum walk algorithms with different coins for searching exceptional configurations on grids and hypercubes, revealing that coin choice limits search success and that exceptional configurations are not inherently quantum.

Contribution

It introduces a modified coin operator capable of successfully searching all configuration types, highlighting the impact of coin choice on quantum walk search limitations.

Findings

Modified coin operator searches all configurations successfully

Exceptional configurations are due to coin choice, not quantum mechanics

Existence of exceptional configurations is a limitation of certain coins

Abstract

There exist two types of configurations of marked vertices on a two-dimensional grid, known as the {\it exceptional configurations}, which are hard to find by the discrete-time quantum walk algorithms. In this article, we provide a comparative study of the quantum walk algorithm with different coins to search these {\it exceptional configurations} on a two-dimensional grid. We further extend the analysis to the hypercube, where only one type of {\it exceptional configurations} are present. Our observation, backed by numerical results, is that our recently proposed modified coin operator is the only coin which can search both types of {\it exceptional configurations} as well as non-{\it exceptional configurations} successfully. As a consequence, we observe that the existence of {\it exceptional configurations} are not a quantum phenomenon, rather a mere limitation of some of the coin operators.