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Robust and efficient eigenstate preparation is a central challenge in quantum simulation in the noisy intermediate-scale quantum (NISQ) era and beyond. The Rodeo Algorithm (RA) [1] offers exponential convergence to a target eigenstate but suffers from poor performance when the initial state has low fidelity with the desired eigenstate, limiting its scalability. In this work, we introduce a fusion method that preconditions the RA by an adiabatic ramp and modular subsystem fusion, enabling high-fidelity state preparation across large many-body systems. Numerical simulations of the spin-1/2 XX chain demonstrate that this hybrid preconditioning restores the RA’s exponential convergence and dramatically reduces computational cost. The method’s efficiency is governed by boundary size, making it ideally suited for 1D and quasi-1D architectures such as trapped-ion chains and neutral-atom arrays. The fusion method thus defines a scalable framework for high-fidelity quantum state preparation across both present and future generations of quantum hardware.
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This content will become publicly available on April 1, 2027
On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials
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.
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- PAR ID:
- 10681647
- Publisher / Repository:
- Springer Nature
- Date Published:
- Journal Name:
- Communications in Mathematical Physics
- Volume:
- 407
- Issue:
- 4
- ISSN:
- 0010-3616
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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