Perfect state transfer in products and covers of graphs

Abstract

A continuous-time quantum walk on a graph $X$ is represented by the complex matrix $\exp (-\mathrm{i}tA)$, where $A$ is the adjacency matrix of $X$ and $t$ is a non-negative time. If the graph models a network of interacting qubits, transfer of state among such qubits throughout time can be formalized as the action of the continuous-time quantum walk operator in the characteristic vectors of the vertices. Here we are concerned with the problem of determining which graphs admit a perfect transfer of state. More specifically, we will study graphs whose adjacency matrix is a sum of tensor products of $01$-matrices, focusing on the case where a graph is the tensor product of two other graphs. As a result, we will construct many new examples of perfect state transfer.

15 pages

References in corpus (4)

• Perfect Transfer of Arbitrary States in Quantum Spin Networks
• Quantum Networks on Cubelike Graphs
• Perfect state transfer in cubelike graphs
• Perfect state transfer on distance-regular graphs and association schemes

Cited by in corpus (3)

• Perfect quantum state transfer using Hadamard diagonalizable graphs
• Continuous-Time Quantum Walks on Dynamic Graphs
• On state transfer in Cayley graphs for abelian groups