Improved Rodeo Algorithm Performance for Spectral Functions and State Preparation

TL;DR

This paper enhances the Rodeo Algorithm's efficiency in spectral analysis and state preparation by introducing a geometric series time sampling method, validated through theoretical analysis and practical demonstrations on various Hamiltonians.

Contribution

It proposes a near-optimal geometric series time sampling strategy to improve Rodeo Algorithm performance across different Hamiltonians, reducing the need for fine-tuning.

Findings

Geometric series of time samples optimize Rodeo Algorithm performance.

The sampling method maintains exponential efficiency for spectral and state preparation tasks.

Practical applicability demonstrated on multiple physical Hamiltonians.

Abstract

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.