Isospectral reductions and quantum walks on graphs
Combinatorics
2022-12-02 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2212.00172,
title = {Isospectral reductions and quantum walks on graphs},
author = {Mark Kempton and John Tolbert},
journal= {arXiv preprint arXiv:2212.00172},
year = {2022}
}