On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials
arXiv:2507.22707 · doi:10.1007/s00220-026-05593-6
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 -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 -order convergence rate is optimal, as previous work has numerically demonstrated that it can be saturated by a specific initial ground state. 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. Our analysis treats the Coulomb potential as an unbounded operator without modification or regularization, and does not rely on spatial discretization, making it compatible with both first- and second-quantized circuit constructions.
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