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arXiv · 2302.01869

Exponentially decaying velocity bounds of quantum walks in periodic fields

Houssam Abdul-Rahman·Günter Stolz
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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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Houssam Abdul-Rahman, Günter Stolz. 2023-02-03. Exponentially decaying velocity bounds of quantum walks in periodic fields. https://arxiv.org/abs/2302.01869

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