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arXiv · 2507.15421

Slow convergence of Trotter decomposition for rotations

Paolo Facchi·Francesco Perrini·Vito Viesti
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Abstract

We study the Trotter approximation for a pair of orbital angular momentum operators, $L_x$ and $L_y$. In particular, we investigate the scaling behavior of the state-dependent Trotter error. We show that for states in the domains of the orbital angular momentum operators the Trotter error scales as $n^{-1}$, where $n$ is the number of time steps. Instead, the convergence rate can be arbitrarily slow for states that do not belong to the domains of the angular momentum operators.

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Paolo Facchi, Francesco Perrini, Vito Viesti. 2025-07-21. Slow convergence of Trotter decomposition for rotations. https://doi.org/10.1016/j.aop.2026.170539

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