State Transfer on Graphs

Abstract

If $X$ is a graph with adjacency matrix $A$, then we define $H(t)$ to be the operator $\exp (itA)$. We say that we have perfect state transfer in $X$ from the vertex $u$ to the vertex $v$ at time $\tau$ if the $uv$-entry of $|H(\tau {)}_{u,v}|=1$. This concept has potential applications in quantum computing. We offer a survey of some of the work on perfect state transfer and related questions. The emphasis is almost entirely on the mathematics.

36 pages, fixed mistake in Corollary 9.3

References in corpus (16)

• Perfect Transfer of Arbitrary States in Quantum Spin Networks
• Quantum Networks on Cubelike Graphs
• Perfect state transfer in cubelike graphs
• Perfect Quantum Routing in Regular Spin Networks
• The Basics of Perfect Communication through Quantum Networks
• Control by quantum dynamics on graphs
• Characterization of circulant graphs having perfect state transfer
• On quantum perfect state transfer in weighted join graphs
• Controllable Subsets in Graphs
• Average mixing of continuous quantum walks
• Universal Mixing of Quantum Walk on Graphs
• Perfect state transfer, integral circulants and join of graphs
• Perfect state transfer, graph products and equitable partitions
• Type-II Matrices and Combinatorial Structures
• Mixing of Quantum Walks on Generalized Hypercubes
• Communication in XYZ All-to-All Quantum Networks with a Missing Link

Cited by in corpus (1)

• Pretty good state transfer on double stars