Quantum walks on Cayley graphs
نویسندگان
چکیده
منابع مشابه
Quantum Walks on Cayley Graphs
We address the problem of the construction of quantum walks on Cayley graphs. Our main motivation is the relationship between quantum algorithms and quantum walks. In particular, we discuss the choice of the dimension of the local Hilbert space and consider various classes of graphs on which the structure of quantum walks may differ. We completely characterise quantum walks on free groups and p...
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A quantum walk, i.e., the quantum evolution of a particle on a graph, is termed scalar if the internal space of the moving particle (often called the coin) has dimension one. Here, we study the existence of scalar quantum walks on Cayley graphs, which are built from the generators of a group. After deriving a necessary condition on these generators for the existence of a scalar quantum walk, we...
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Previous authors have shown bounds on mixing time of random walks on finite undirected Cayley graphs, both with and without self-loops. We extend this to the most general case by showing that a similar bound holds for walks on all finite directed Cayley graphs. These are shown by use of two new canonical path theorems for mixing time of non-reversible Markov chains. The first result is related ...
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We consider the definition of quantum walks on directed graphs. Call a directed graph reversible if, for each pair of vertices (vi, vj), if vi is connected to vj then there is a path from vj to vi. We show that reversibility is a necessary and sufficient condition for a directed graph to allow the notion of a discrete-time quantum walk, and discuss some implications of this condition. We presen...
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We review some recent results concerning recurrence and transience for branching random walks in random environment on ddimensional lattices and on trees. We obtain some generalizations of these results for the case when the branching random walk in random environment takes place on arbitrary infinite connected Cayley graph.
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2005
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/39/3/011