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arXiv · 2511.13409

On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks

Benjamin Hinrichs·Pascal Mittenbühler
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Abstract

We study the convergence rate of translation-invariant discrete-time quantum dynamics on a one-dimensional lattice. We prove that the cumulative distributions function of the ballistically scaled position $X(n)/{n}$ after $n$ steps converges at a rate of $n^{-1/3}$ in the L\'evy metric as $n\to\infty$. In the special case of step-coin quantum walks with two-dimensional coin space, we recover the same convergence rate for the supremum distance and prove optimality.

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Benjamin Hinrichs, Pascal Mittenbühler. 2025-11-17. On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks. https://arxiv.org/abs/2511.13409

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