Improved Rodeo Algorithm Performance for Spectral Functions and State Preparation

The Rodeo Algorithm is a quantum computing method for computing the energy spectrum of a Hamiltonian and preparing its energy eigenstates. We discuss how to improve the performance of the rodeo algorithm for each of these two applications. In particular, we demonstrate that using a geometric series of time samples offers a near-optimal optimization space for a given total runtime by studying the Rodeo Algorithm performance on a model Hamiltonian representative of gapped many-body quantum systems. Analytics explain the performance of this time sampling and the conditions for it to maintain the established exponential performance of the Rodeo Algorithm. We finally demonstrate this sampling protocol on various physical Hamiltonians, showing its practical applicability. Our results suggest that geometric series of times provide a practical, near-optimal, and robust time-sampling strategy for quantum state preparation with the Rodeo Algorithm across varied Hamiltonians without requiring model-specific fine-tuning.

💡 Research Summary

The paper investigates how to enhance the performance of the Rodeo Algorithm (RA), a quantum algorithm used both for extracting the energy spectrum of a Hamiltonian and for preparing its eigenstates. The authors focus on the choice of time‑sampling, which is a critical factor determining how efficiently unwanted eigencomponents are suppressed. They introduce two quantitative metrics: (i) the single‑step success probability p(E,t)=cos²