Exponentially decaying velocity bounds of quantum walks in periodic fields

• URL: http://arxiv.org/abs/2302.01869v1
• Date: Fri, 3 Feb 2023 17:15:15 GMT
• Title: Exponentially decaying velocity bounds of quantum walks in periodic fields
• Authors: Houssam Abdul-Rahman, G\"unter Stolz
• Abstract summary: We consider a class of discrete-time one-dimensional quantum walks, associated with a CMV unitary matrix, in the presence of a local field. We show that for a certain range for $t$, the corresponding velocity can be made arbitrarily small by introducing a periodic local field with a sufficiently large period.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a class of discrete-time one-dimensional quantum walks, associated with CMV unitary matrices, in the presence of a local field. This class is parametrized by a transmission parameter $t\in[0,1]$. We show that for a certain range for $t$, the corresponding asymptotic velocity can be made arbitrarily small by introducing a periodic local field with a sufficiently large period. In particular, we prove an upper bound for the velocity of the $n$-periodic quantum walk that is decaying exponentially in the period length $n$. Hence, localization-like effects are observed even after a long number of quantum walk steps when $n$ is large.

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