Quantum walks and the size of the graph
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Universidade Federal de Minas Gerais
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Artigo de periódico
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Resumo
A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur. Among other things, we show that, in the adjacency matrix quantum walk model, the number of edges is bounded below by a cubic function on the eccentricity of a periodic vertex. This gives some idea on the shape of a graph that would admit periodicity or perfect state transfer. We also raise some extremal type of questions in the end that could lead to future research
Abstract
Assunto
Teoria dos grafos, Análise espectral, Computação quântica
Palavras-chave
Quantum walk, Spectral bounds, State transfer
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Endereço externo
https://www.sciencedirect.com/science/article/pii/S0012365X1830116X