Tuesday, May 28, 2013

1305.6078 (Mauro Faccin et al.)

Degree Distribution in Quantum Walks on Complex Networks    [PDF]

Mauro Faccin, Tomi Johnson, Jacob Biamonte, Sabre Kais, Piotr Migdał
We relate the average long time probability of finding a quantum walker at a node to that for a corresponding classical walk. The latter is proportional to the node degree. We replace the state dependence of quantum evolution by a partial order, bounding the quantumness of the walker in terms of the energy of the initial state and the spectral gap of the complex network. For a uniform initial state, we identify complex network classes and regimes for which the classical degree-dependent result is recovered and others for which quantum effects dominate. The importance of quantum effects, or the quantumness of a complex network, is given by the R\'enyi entropy of order 1/2 of the normalized weighted degrees, which can be upper bounded by the Shannon entropy.
View original: http://arxiv.org/abs/1305.6078

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