Recurrence and Pólya number of quantum walks

Details Recurrence and Pólya number of quantum walks Recurrence and Pólya number of quantum walks

2007-05-14

arxiv.org/abs/0705.1991v2

Phys. Rev. Lett. 100, 020501 (2008)

Physics

Quantum Physics

Scientific paper

10.1103/PhysRevLett.100.020501

We analyze the recurrence probability (P\'olya number) for d-dimensional unbiased quantum walks. A sufficient condition for a quantum walk to be recurrent is derived. As a by-product we find a simple criterion for localisation of quantum walks. In contrast to classical walks, where the P\'olya number is characteristic for the given dimension, the recurrence probability of a quantum walk depends in general on the topology of the walk, choice of the coin and the initial state. This allows to change the character of the quantum walk from recurrent to transient by altering the initial state.

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