Perfect state transfer by means of discrete-time quantum walk search algorithms on highly symmetric graphs

Abstract

Perfect state transfer between two marked vertices of a graph by means of discrete-time quantum walk is analyzed. We consider the quantum walk search algorithm with two marked vertices, sender and receiver. It is shown by explicit calculation that for the coined quantum walks on star graph and complete graph with self-loops perfect state transfer between the sender and receiver vertex is achieved for arbitrary number of vertices $N$ in $O(\sqrt{N})$ steps of the walk. Finally, we show that Szegedy's walk with queries on complete graph allows for state transfer with unit fidelity in the limit of large $N$.

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• Quantum Simulation of Neutrino Oscillation and Dirac Particle Dynamics in Curved Space-time
• Search and state transfer between hubs by quantum walks
• Perfect State Transfer in Weighted Cubelike Graphs
• Periodicity of Grover walks on generalized Bethe trees
• Quantum Search on Simplicial Complexes