Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773331 | Linear Algebra and its Applications | 2017 | 17 Pages |
Abstract
A continuous-time quantum walk on a graph is a matrix-valued function expâ¡(âiAt) over the reals, where A is the adjacency matrix of the graph. Such a quantum walk has universal perfect state transfer if for all vertices u,v, there is a time where the (v,u) entry of the matrix exponential has unit magnitude. We prove new characterizations of graphs with universal perfect state transfer. This extends results of Cameron et al. (2014) [3]. Also, we construct non-circulant families of graphs with universal perfect state transfer. All prior known constructions were circulants. Moreover, we prove that if a circulant, whose order is prime, prime squared, or a power of two, has universal perfect state transfer then its underlying graph must be complete. This is nearly tight since there are universal perfect state transfer circulants with non-prime-power order where some edges are missing.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Erin Connelly, Nathaniel Grammel, Michael Kraut, Luis Serazo, Christino Tamon,