期刊
INTERNATIONAL JOURNAL OF QUANTUM INFORMATION
卷 5, 期 3, 页码 417-430出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219749907002918
关键词
circulant graphs; integral graphs; periodic dynamics; perfect state transfer
The intention of the paper is to move a step towards a classification of network topologies that exhibit periodic quantum dynamics. We show that the evolution of a quantum system whose hamiltonian is identical to the adjacency matrix of a circulant graph is periodic if and only if all eigenvalues of the graph are integers (that is, the graph is integral). Motivated by this observation, we focus on relevant properties of integral circulant graphs. Specifically, we bound the number of vertices of integral circulant graphs in terms of their degree, characterize bipartiteness and give exact bounds for their diameter. Additionally, we prove that circulant graphs with odd order do not allow perfect state transfer.
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