2022/11/30 by Mark Kempton, Kempton, Mark, John Tolbert +1
Computer Science · #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Computing Algorithms and Architecture
paper · pdf · doi:10.48550/arxiv.2212.00172
openalex publication_date 2022/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.