Slow convergence of Trotter decomposition for rotations

2025/07/21 by Facchi, Paolo, Perrini, Francesco, Viesti, Vito
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2507.15421

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 time discretization. Instead, the convergence rate can be arbitrarily slow for states that do not belong to the domains of all three angular momentum operators simultaneously.

Citations

• Convergence Rates for the Trotter Splitting for Unbounded Operators
• Strong error bounds for Trotter and strang-splittings and their implications for quantum chemistry
• Spectral Analysis of Product Formulas for Quantum Simulation
• On the product of semi-groups of operators

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