Quantum walks on Cayley graphs

Details Quantum walks on Cayley graphs Quantum walks on Cayley graphs

2005-03-08

arxiv.org/abs/quant-ph/0503078v4

J. Phys. A: Math. Gen. 39 (2006) 585-599

Physics

Quantum Physics

J. Phys. A (accepted for publication)

Scientific paper

10.1088/0305-4470/39/3/011

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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