Line graph

Algorithm

Pure mathematics

Discrete mathematics

Cyclic group

Materials science

Voltage graph

Abelian group

Circulant graph

Computation

Circulant matrix

Parallel computing

Computer science

Cayley graph

Free abelian group

Transfer (computing)

Nanotechnology

Cayley transform

Elementary abelian group

Graph

Mathematics

Characterization (materials science)

Cayley's theorem

Rank of an abelian group

Combinatorics

Algebra over a field

State (computer science)

Linear Algebra and its Applications

Perfect state transfer (PST) has great significance due to its applications in quantum information processing and quantum computation. In this paper we present a characterization of the connected simple Cayley graph Γ=Cay(G,S) having PST, where G is an abelian group and S is a non-empty set of G. We show that many previous results on periodicity and existence of PST of circulant graphs (where the underlying group G is cyclic) and cubelike graphs (G=(F2n,+)) can be derived or generalized to arbitrary abelian case in unified and more simple ways from our characterization. We also get several new results including answers to some questions raised before.

Perfect state transfer on abelian Cayley graphs