Fundamentals of fractional revival in graphs

Chan, Ada; Coutinho, Gabriel; Drazen, Whitney; Eisenberg, Or; Godsil, Chris; Lippner, Gábor; Kempton, Mark; Tamon, Christino; Zhan, Hanmeng

doi:10.1016/j.laa.2022.09.010

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Quantum Walks1

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Cited by 6 publications

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“…for some U ′ . We call this fractional revival on S with respect to H. See [7,8] for more details. Note that PST from u to v is FR with respect to the matrix 0 γ γ 0 on the set {u, v}.…”

Section: Quantum Walksmentioning

confidence: 99%

Isospectral reductions and quantum walks on graphs

Kempton,

Tolbert

2024

Algebraic Combinatorics

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We give a new formula for computing the isospectral reduction of a matrix (and graph) down to a submatrix (or subgraph). Using this, we generalize the notion of isospectral reductions. In addition, we give a procedure for constructing a matrix whose isospectral reduction down to a submatrix is given. We also prove that the isospectral reduction completely determines the restriction of the quantum walk transition matrix to a subset. Using these, we construct new families of simple graphs exhibiting perfect quantum state transfer.

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Section: Quantum Walksmentioning

confidence: 99%