NDLI: No Laplacian Perfect State Transfer in Trees

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Liu, Henry Coutinho, Gabriel
Copyright Year	2015
Abstract	We consider a system of qubits coupled via nearest-neighbor interaction governed by the Heisenberg Hamiltonian. We further suppose that all coupling constants are equal to 1. We are interested in determining which graphs allow for a transfer of quantum state with fidelity equal to 1. To answer this question, it is enough to consider the action of the Laplacian matrix of the graph in a vector space of suitable dimension. Our main result is that if the underlying graph is a tree with more than two vertices, then perfect state transfer does not happen. We also explore related questions, such as what happens in bipartite graphs and graphs with an odd number of spanning trees. Finally, we consider the model based on the $XY$-Hamiltonian, whose action is equivalent to the action of the adjacency matrix of the graph. In this case, we conjecture that perfect state transfer does not happen in trees with more than three vertices.
Starting Page	2179
Ending Page	2188
Page Count	10
File Format	PDF
ISSN	08954801
DOI	10.1137/140989510
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	4
Volume Number	29
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2015-11-10
Access Restriction	Subscribed
Subject Keyword	quantum walks Trees Quantum computation Matrix exponential and similar functions of matrices Graphs and linear algebra perfect state transfer Laplacian matrix trees
Content Type	Text
Resource Type	Article
Subject	Mathematics

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