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Open Quantum Systems Decoherence Quantum Simulation

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

arXiv

Authors: Benjamin Hinrichs, Pascal Mittenbühler

Year

2025

Paper ID

17037

Status

Preprint

Abstract Read

~2 min

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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 Lévy metric as n→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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We study the convergence rate of translation-invariant discrete-time quantum dynamics on a one-dimensional lattice.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2511.13409 [2] arXiv https://arxiv.org/abs/2511.13409 [3] Publisher https://arxiv.org/abs/2511.13409

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