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- W4320167495 abstract "Some of the quantum searching models have been given by perturbed quantum walks. Driving some perturbed quantum walks, we may quickly find one of the targets with high probability. In this paper, we construct a quantum searching model finding one of the edges of a given subgraph in a complete graph. How to construct our model is that we label the arcs by $+1$ or $-1$, and define a perturbed quantum walk by the sign function on the set of arcs. After that, we detect one of the edges labeled $-1$ by the induced sign function as fast as possible. This idea was firstly proposed by Segawa et al. in 2021. They only addressed the case where the subgraph forms a matching, and obtained by a combinatorial argument that the time of finding one of the edges of the subgraph is quadratically faster than a classical searching model. In this paper, we show that the model is valid for any subgraph, i.e., we obtain by spectral analysis a quadratic speed-up for finding one of the edges of the subgraph in a complete graph." @default.
- W4320167495 created "2023-02-13" @default.
- W4320167495 creator A5011263715 @default.
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- W4320167495 date "2022-02-03" @default.
- W4320167495 modified "2023-09-29" @default.
- W4320167495 title "A quantum searching model finding one of the edges of a subgraph in a complete graph" @default.
- W4320167495 doi "https://doi.org/10.48550/arxiv.2202.01464" @default.
- W4320167495 hasPublicationYear "2022" @default.
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