On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912847907258368 |
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| author | Hinrichs, Benjamin Mittenbühler, Pascal |
| author_facet | Hinrichs, Benjamin Mittenbühler, Pascal |
| contents | 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 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_13409 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks Hinrichs, Benjamin Mittenbühler, Pascal Mathematical Physics Quantum Physics 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 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. |
| title | On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2511.13409 |