Quantum walk search for exceptional configurations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908431726673920 |
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| author | Giri, Pulak Ranjan |
| author_facet | Giri, Pulak Ranjan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02457 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum walk search for exceptional configurations Giri, Pulak Ranjan Quantum Physics 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. |
| title | Quantum walk search for exceptional configurations |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2507.02457 |