Pólya number of continuous-time quantum walks

Abstract

We propose a definition for the Pólya number of continuous-time quantum walks to characterize their recurrence properties. The definition involves a series of measurements on the system, each carried out on a different member from an ensemble in order to minimize the disturbance caused by it. We examine various graphs, including the ring, the line, higher dimensional integer lattices and a number of other graphs and calculate their Pólya number. For the timing of the measurements a Poisson process as well as regular timing are discussed. We find that the speed of decay for the probability at the origin is the key for recurrence.

8 pages, no figures. Accepted for publication in Physical Review A

References in corpus (13)

• Universal computation by quantum walk
• On the relationship between continuous- and discrete-time quantum walk
• Connecting the discrete and continuous-time quantum walks
• Recurrence and Pólya number of quantum walks
• Quantum walks with infinite hitting times
• Recurrence properties of unbiased coined quantum walks on infinite $d$-dimensional lattices
• Hitting time for the continuous quantum walk
• Efficiency of quantum and classical transport on graphs
• Exact analytical results for quantum walks on star graph
• Dynamics of continuous-time quantum walks in restricted geometries
• Continuous-time quantum walks on one-dimension regular networks
• Investigation of continuous-time quantum walk on root lattice $A_n$ and honeycomb lattice
• Universal Behavior of Quantum Walks with Long-Range Steps

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• Optimal Measurement Protocols in Quantum Zeno Effect
• Recurrence and Polya number of general one-dimensional random walks
• Shining Light on Quantum Transport in Fractal Networks
• Recurrence in discrete-time quantum stochastic walks
• On the Recurrence Character of the Hadamard walk in the Plane