Quantum state revivals in quantum walks on cycles
arXiv:1405.7345 · doi:10.1016/j.rinp.2014.10.001
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 (15)
- Quantum random walks - an introductory overview
- Quantum Computation and Decision Trees
- A Quantum Random Walk Search Algorithm
- Universal computation by quantum walk
- Universal quantum computation using the discrete time quantum walk
- Implementing the quantum random walk
- Controlling discrete quantum walks: coins and intitial states
- Quantum Walks driven by many coins
- A random walk approach to quantum algorithms
- Quantum algorithms for hidden nonlinear structures
- Universal quantum computation by discontinuous quantum walk
- Full-revivals in 2-D Quantum Walks
- Pólya number of continuous-time quantum walks
- Fractional recurrence in discrete-time quantum walk
- 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