An Infinite Family of Circulant Graphs with Perfect State Transfer in Discrete Quantum Walks

Abstract

We study perfect state transfer in Kendon's model of discrete quantum walks. In particular, we give a characterization of perfect state transfer purely in terms of the graph spectra, and construct an infinite family of $4$-regular circulant graphs that admit perfect state transfer. Prior to our work, the only known infinite families of examples were variants of cycles and diamond chains.

References in corpus (5)

• Universal computation by quantum walk
• Perfect Transfer of Arbitrary States in Quantum Spin Networks
• Perfect State Transfer: Beyond Nearest-Neighbor Couplings
• Strongly Cospectral Vertices
• Periodicity of Grover walks on distance-regular graphs

Cited by in corpus (2)

• Quantum Walks on Embeddings
• Discrete-Time Quantum Walks and Graph Structures