Quantum walk search for exceptional configurations
arXiv:2507.02457 · doi:10.1142/S0219749924500321
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.
9 pages, 7 figures, Published in IJQI
References in corpus (8)
- Spatial search by quantum walk
- Faster quantum walk algorithm for the two dimensional spatial search
- Spatial search and the Dirac equation
- Connectivity is a Poor Indicator of Fast Quantum Search
- Stationary States in Quantum Walk Search
- Generalized exceptional quantum walk search
- Quantum walk search by Grover search on coin space
- Quantum walk search on a two-dimensional grid with extra edges