Related papers: Irrational quantum walks

Irrational quantum walks

URL: http://arxiv.org/abs/2208.08971v1
Date: Thu, 18 Aug 2022 17:21:47 GMT
Title: Irrational quantum walks
Authors: Gabriel Coutinho, Pedro Ferreira Baptista, Chris Godsil, Thom\'as Jung Spier, Reinhard Werner
Abstract summary: We develop theory to study any quantum walk generated by an integral Hamiltonian. We use our methods to study geometric properties of beautiful curves arising from entries of the quantum walk matrix.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The adjacency matrix of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. Although the entries of the adjacency matrix are integers, its eigenvalues are generally irrational and, because of this, the behaviour of the walk is typically not periodic. In consequence we can usually only compute numerical approximations to parameters of the walk. In this paper, we develop theory to exactly study any quantum walk generated by an integral Hamiltonian. As a result, we provide exact methods to compute the average of the mixing matrices, and to decide whether pretty good (or almost) perfect state transfer occurs in a given graph. We also use our methods to study geometric properties of beautiful curves arising from entries of the quantum walk matrix, and discuss possible applications of these results.

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