Quantum walk search for exceptional configurations

There exist two types of configurations of marked vertices on a two-dimensional grid, known as the 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 exceptional configurations on a two-dimensional grid. We further extend the analysis to the hypercube, where only one type of 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 exceptional configurations as well as nonexceptional configurations successfully. As a consequence, we observe that the existence of exceptional configurations are not a quantum phenomenon, rather a mere limitation of some of the coin operators.