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

• URL: http://arxiv.org/abs/2511.13409v1
• Date: Mon, 17 Nov 2025 14:21:49 GMT
• Title: On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks
• Authors: Benjamin Hinrichs, Pascal Mittenbühler,
• Abstract summary: We study the convergence rate of translation-invariant discrete-time quantum dynamics on a one-dimensional lattice.<n>In the special case of step-coin quantum walks with two-dimensional coin space, we recover the same convergence rate for the supremum distance.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\mathbb X(n)/{n}$ after $n$ steps converges at a rate of $n^{-1/3}$ in the Lévy 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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