Hierarchical Fusion Method for Scalable Quantum Eigenstate Preparation

TL;DR

This paper introduces a hierarchical fusion method that enhances the Rodeo Algorithm for scalable quantum eigenstate preparation, demonstrating improved efficiency and robustness in large systems through adiabatic preconditioning and subsystem building.

Contribution

The authors develop a hybrid approach combining adiabatic ramping with the Rodeo Algorithm, enabling exponential convergence in large-scale quantum systems.

Findings

The fusion method maintains exponential convergence across system sizes.

It offers a computational cost advantage for high-precision state preparation.

Numerical simulations validate robustness and scalability of the approach.

Abstract

Robust and efficient eigenstate preparation is a central challenge in quantum simulation. The Rodeo Algorithm (RA) offers exponential convergence to a target eigenstate but suffers from poor performance when the initial state has low overlap with the desired eigenstate, hindering the applicability of the original algorithm to larger systems. In this work, we introduce a fusion method that preconditions the RA state by an adiabatic ramp to overcome this limitation. By incrementally building up large systems from exactly solvable subsystems and using adiabatic preconditioning to enhance intermediate state overlaps, we ensure that the RA retains its exponential convergence even in large-scale systems. We demonstrate this hybrid approach using numerical simulations of the spin- 1/2 XX model and find that the Rodeo Algorithm exhibits robust exponential convergence across system sizes. We benchmark against using only an adiabatic ramp as well as using the unmodified RA, finding that for state preparation precision at the level of $10^{-3}$ infidelity or better there a decisive computational cost advantage to the fusion method. These results together demonstrate the scalability and effectiveness of the fusion method for practical quantum simulations.