Perfect state transfer on distance-regular graphs and association schemes

Abstract

We consider the representation of a continuous-time quantum walk in a graph $X$ by the matrix $\exp (itA(X))$. We provide necessary and sufficient criteria for distance-regular graphs and, more generally, for graphs in association schemes to have perfect state transfer. Using these conditions, we provide several new examples of perfect state transfer in simple graphs.

32 pages

References in corpus (5)

• Universal computation by quantum walk
• Exponential algorithmic speedup by quantum walk
• Quantum Networks on Cubelike Graphs
• Perfect state transfer in cubelike graphs
• Perfect state transfer over distance-regular spin networks

Cited by in corpus (20)

• Distance-regular graphs
• Eigenvalues of Cayley graphs
• No Laplacian Perfect State Transfer in Trees
• Strongly Cospectral Vertices
• Perfect state transfer in products and covers of graphs
• Perfect State Transfer on NEPS of the path P3
• Entanglement of Free Fermions on Hadamard Graphs
• Quantum state transfer between twins in weighted graphs
• An Infinite Family of Circulant Graphs with Perfect State Transfer in Discrete Quantum Walks
• Unifying quantum spatial search, state transfer and uniform sampling on graphs: simple and exact
• Quantum walk state transfer on a hypercube
• Perfect State Transfer on Weighted Graphs of the Johnson Scheme
• A New Perspective on the Average Mixing Matrix
• Fractional Revival and Association Schemes
• Continuous-time Quantum Walks on Cayley Graphs of Extraspecial Groups
• Search and state transfer between hubs by quantum walks
• Perfect state transfer in two dimensions and the bivariate dual-Hahn polynomials
• Perfect state transfer in NEPS of complete graphs
• Quantum state transfer on distance regular spin networks with intrinsic decoherence
• Uniform mixing on integral abelian Cayley graph