On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910080445710336 |
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| author | Fang, Di Wu, Xiaoxu Soffer, Avy |
| author_facet | Fang, Di Wu, Xiaoxu Soffer, Avy |
| contents | 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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22707 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials Fang, Di Wu, Xiaoxu Soffer, Avy Quantum Physics Mathematical Physics 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 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. |
| title | On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2507.22707 |