Quantum Walk Search on Complete Multipartite Graph with Multiple Marked Vertices
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929530175750144 |
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| author | Chen, Ningxiang Li, Meng Sun, Xiaoming |
| author_facet | Chen, Ningxiang Li, Meng Sun, Xiaoming |
| contents | Quantum walk is a potent technique for building quantum algorithms. This paper examines the quantum walk search algorithm on complete multipartite graphs with multiple marked vertices, which has not been explored before. Two specific cases of complete multipartite graphs are probed in this paper, and in both cases, each set consists of an equal number of vertices. We employ the coined quantum walk model and achieve quadratic speedup with a constant probability of finding a marked vertex. Furthermore, we investigate the robust quantum walk of two cases and demonstrate that even with an unknown number of marked vertices, it is still possible to achieve a quadratic speedup compared to classical algorithms and the success probability oscillates within a small range close to 1. This work addresses the overcooking problem in quantum walk search algorithms on some complete multipartite graphs. We also provide the numerical simulation and circuit implementation of our quantum algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04924 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Walk Search on Complete Multipartite Graph with Multiple Marked Vertices Chen, Ningxiang Li, Meng Sun, Xiaoming Quantum Physics Quantum walk is a potent technique for building quantum algorithms. This paper examines the quantum walk search algorithm on complete multipartite graphs with multiple marked vertices, which has not been explored before. Two specific cases of complete multipartite graphs are probed in this paper, and in both cases, each set consists of an equal number of vertices. We employ the coined quantum walk model and achieve quadratic speedup with a constant probability of finding a marked vertex. Furthermore, we investigate the robust quantum walk of two cases and demonstrate that even with an unknown number of marked vertices, it is still possible to achieve a quadratic speedup compared to classical algorithms and the success probability oscillates within a small range close to 1. This work addresses the overcooking problem in quantum walk search algorithms on some complete multipartite graphs. We also provide the numerical simulation and circuit implementation of our quantum algorithm. |
| title | Quantum Walk Search on Complete Multipartite Graph with Multiple Marked Vertices |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.04924 |