On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials

• URL: http://arxiv.org/abs/2507.22707v1
• Date: Wed, 30 Jul 2025 14:17:08 GMT
• Title: On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials
• Authors: Di Fang, Xiaoxu Wu, Avy Soffer,
• Abstract summary: We analyze many-body quantum systems with Coulomb interactions.<n>We prove that Trotterization for such Hamiltonians achieves a $1/4$-order convergence rate.
• Score: 1.2289361708127877
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Efficient simulation of many-body quantum systems is central to advances in physics, chemistry, and quantum computing, with a key question being whether the simulation cost scales polynomially with the system size. In this work, we analyze many-body quantum systems with Coulomb interactions, which are fundamental to electronic and molecular systems. We prove that Trotterization for such unbounded Hamiltonians achieves a $1/4$-order convergence rate, with explicit polynomial dependence on the number of particles. The result holds for all initial wavefunctions in the domain of the Hamiltonian, and the $1/4$-order convergence rate is optimal, as previous studies have shown that it can be saturated by a specific initial eigenstate. The main challenges arise from the many-body structure and the singular nature of the Coulomb potential. Our proof strategy differs from prior state-of-the-art Trotter analyses, addressing both difficulties in a unified framework.

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