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Slow convergence of Trotter decomposition for rotations
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We study the Trotter approximation for a pair of orbital angular momentum operators, Lx and Ly. 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.
Title: Slow convergence of Trotter decomposition for rotations
Description:
We study the Trotter approximation for a pair of orbital angular momentum operators, Lx and Ly.
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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