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Isospectral reductions and quantum walks on graphs
Kempton, Mark1; Tolbert, John2
1 Brigham Young University Department of Mathematics Provo UT 84602 (USA)
2 Wake Forest University Department of Mathematics Winston-Salem NC 27587 (USA)
Algebraic Combinatorics, Volume 7 (2024) no. 1, pp. 225-243.

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.

Received:
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Accepted:
Published online:
DOI: 10.5802/alco.333
Classification: 05C50, 15A18
Keywords: isospectral reduction, equitable partition, quantum walk, perfect state transfer

Kempton, Mark 1; Tolbert, John 2

1 Brigham Young University Department of Mathematics Provo UT 84602 (USA)
2 Wake Forest University Department of Mathematics Winston-Salem NC 27587 (USA)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Kempton, Mark; Tolbert, John. Isospectral reductions and quantum walks on graphs. Algebraic Combinatorics, Volume 7 (2024) no. 1, pp. 225-243. doi : 10.5802/alco.333. https://alco.centre-mersenne.org/articles/10.5802/alco.333/

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