Mark Kempton

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In this paper we study quantum state transfer (also called quantum tunneling) on graphs when there is a potential function on the vertex set. We present two main results. First, we show that for paths of length greater than three, there is no potential on the vertices of the path for which perfect state transfer between the endpoints can occur. In(More)
We give a clustering algorithm for connection graphs, that is, weighted graphs in which each edge is associated with a d-dimensional rotation. The problem of interest is to identify subsets of small Cheeger ratio and which have a high level of consistency, i.e. that have small edge boundary and the rotations along any distinct paths joining two vertices are(More)
We study pretty good single-excitation quantum state transfer (i.e., state transfer that becomes arbitrarily close to perfect) between particles in symmetric spin networks, in the presence of an energy potential induced by a magnetic field. In particular, we show that if a network admits an involution that fixes at least one node or at least one link, then(More)
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