{"date_created":"2026-01-16T08:59:54Z","date_updated":"2026-01-16T09:00:31Z","project":[{"_id":"266","name":"PhoQC: Photonisches Quantencomputing"}],"type":"preprint","department":[{"_id":"799"}],"author":[{"id":"99427","first_name":"Benjamin","last_name":"Hinrichs","orcid":"0000-0001-9074-1205","full_name":"Hinrichs, Benjamin"},{"full_name":"Mittenbühler, Pascal","last_name":"Mittenbühler","first_name":"Pascal"}],"status":"public","abstract":[{"text":"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.","lang":"eng"}],"language":[{"iso":"eng"}],"external_id":{"arxiv":["2511.13409"]},"user_id":"99427","publication":"arXiv:2511.13409","citation":{"short":"B. Hinrichs, P. Mittenbühler, ArXiv:2511.13409 (2025).","apa":"Hinrichs, B., &#38; Mittenbühler, P. (2025). On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks. In <i>arXiv:2511.13409</i>.","chicago":"Hinrichs, Benjamin, and Pascal Mittenbühler. “On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks.” <i>ArXiv:2511.13409</i>, 2025.","ama":"Hinrichs B, Mittenbühler P. On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks. <i>arXiv:251113409</i>. Published online 2025.","ieee":"B. Hinrichs and P. Mittenbühler, “On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks,” <i>arXiv:2511.13409</i>. 2025.","mla":"Hinrichs, Benjamin, and Pascal Mittenbühler. “On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks.” <i>ArXiv:2511.13409</i>, 2025.","bibtex":"@article{Hinrichs_Mittenbühler_2025, title={On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks}, journal={arXiv:2511.13409}, author={Hinrichs, Benjamin and Mittenbühler, Pascal}, year={2025} }"},"title":"On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks","_id":"63647","year":"2025"}