Quantum search of many vertices on the joined complete graph |
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Institution: | Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics&Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China |
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Abstract: | The quantum search on the graph is a very important topic. In this work, we develop a theoretic method on searching of single vertex on the graph $Phys. Rev. Lett$. 114 110503 (2015)], and systematically study the search of many vertices on one low-connectivity graph, the joined complete graph. Our results reveal that, with the optimal jumping rate obtained from the theoretical method, we can find such target vertices at the time $O\left({\sqrt N } \right)$, where $N$ is the number of total vertices. Therefore, the search of many vertices on the joined complete graph possessing quantum advantage has been achieved. |
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Keywords: | quantum search the joined complete graph quantum walk many vertices |
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