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Quantum walks on Cayley graphs
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Quantum walks on Cayley graphs
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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 present partial results on more general cases. Some examples are given, including a family of quantum walks on the hypercube involving a Clifford Algebra.
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Cited by 1 Pith paper
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Quantum random walks on d-regular graphs with Haar-random coin operators
Haar-random coin quantum walks on d-regular graphs yield a non-ergodic averaged channel that depolarizes the coin while preserving forever-measurable initial-state information in the vertex subspace for Cayley graphs ...
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