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arXiv · 2507.02457

Quantum walk search for exceptional configurations

Pulak Ranjan Giri
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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.

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Pulak Ranjan Giri. 2025-07-03. Quantum walk search for exceptional configurations. https://doi.org/10.1142/s0219749924500321

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