Quantum walk search for exceptional configurations

• URL: http://arxiv.org/abs/2507.02457v1
• Date: Thu, 03 Jul 2025 09:14:10 GMT
• Title: Quantum walk search for exceptional configurations
• Authors: Pulak Ranjan Giri,
• Abstract summary: We provide a comparative study of the quantum walk algorithm with different coins to search it exceptional configurations on a two-dimensional grid.<n>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 successfully.<n>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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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