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) [Choi et al., Phys. Rev. Lett. 127, 040505 (2021)] 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 one-dimensional (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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• Quantum algorithms
• Quantum algorithms & computation
• Quantum algorithms for chemical calculations
• Quantum computation
• Quantum simulation