Quantum state revivals in quantum walks on cycles

Abstract

Recurrence in the classical random walk is well known and described by the Pólya number. For quantum walks, recurrence is similarly understood in terms of the probability of a localized quantum walker to return to its origin. Under certain circumstances the quantum walker may also return to an arbitrary initial quantum state in a finite number of steps. Quantum state revivals in quantum walks on circles using coin operators which are constant in time and uniform across the path have been described before but only incompletely. In this paper we find the general conditions for which full-quantum state revival will occur.

19 pages, 3 figures

References in corpus (5)

• Universal computation by quantum walk
• A random walk approach to quantum algorithms
• Quantum algorithms for hidden nonlinear structures
• Full-revivals in 2-D Quantum Walks
• Quantum diffusion on a cyclic one dimensional lattice

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• Improving quantum walk metrology with split-step quantum walk
• Controlling quantum chaos via Parrondo strategies on noisy intermediate-scale quantum hardware