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An algorithm to factorize quantum walks into shift and coin operations. (English) Zbl 1504.47061

Summary: We provide an algorithm that factorizes one-dimensional quantum walks on an arbitrary but fixed cell structure into a protocol of two basic operations: a fixed conditional shift that transports particles between cells and suitable coin operators that act locally in each cell. This allows to tailor quantum walk protocols to any experimental set-up by rephrasing it on the cell structure determined by the experimental limitations. We give the example of a walk defined on a qutrit chain compiled to run on a qubit chain.

MSC:

47B93 Operators arising in mathematical physics
15A23 Factorization of matrices
81S99 General quantum mechanics and problems of quantization
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
81R15 Operator algebra methods applied to problems in quantum theory
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