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Stationary measure for two-state space-inhomogeneous quantum walk in one dimension. (English) Zbl 1419.60064

Summary: We consider the two-state space-inhomogeneous coined quantum walk (QW) in one dimension. For a general setting, we obtain the stationary measure of the QW by solving the eigenvalue problem. As a corollary, stationary measures of the multi-defect model and space-homogeneous QW are derived. The former is a generalization of the previous works on one-defect model and the latter is a generalization of the result given by N. Konno and M. Takei [“The non-uniform stationary measure for discrete-time quantum walks in one dimension”, Quantum Inf. Comput. 15 1060–1075 (2015)].

MSC:

60K40 Other physical applications of random processes
81P68 Quantum computation
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