K. Barr, T. Proctor, B. Hanson, S. Martiel, V. Pavlovic, A. Bullivant, V. Kendon
We introduce a new model of the discrete time quantum walk, the self-avoiding quantum walk, which is not allowed to step back onto a position which it has just occupied. This allows us to simulate a dimer and we achieve it by introducing a new type of coin operator. We describe its basic properties and provide numerical evidence that the standard deviation of the walker is constant regardless of the initial state. This contrasts strongly with previously studied coins such as the Grover operator, where the initial condition can be used to control the standard deviation of the walker.
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http://arxiv.org/abs/1303.1966
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