Demonstration of the rodeo algorithm on a quantum computer
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10050_2024_1373_ReferencePDF.pdf
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Author(s)
Qian, Zhengrong
Watkins, Jacob
Given, Gabriel
Bonitati, Joey
Choi, Kenneth
Lee, Dean
Date Issued
July 20, 2024
Journal
The European Physical Journal A
Publisher
Springer Berlin Heidelberg
Citation
Qian, Z., Watkins, J., Given, G. et al. Demonstration of the rodeo algorithm on a quantum computer. Eur. Phys. J. A 60, 151 (2024).
Version
Author's final manuscript
Abstract
The rodeo algorithm is an efficient algorithm for eigenstate preparation and eigenvalue estimation for any observable on a quantum computer. This makes it a promising tool for studying the spectrum and structure of atomic nuclei as well as other fields of quantum many-body physics. The only requirement is that the initial state has sufficient overlap probability with the desired eigenstate. While it is exponentially faster than well-known algorithms such as phase estimation and adiabatic evolution for eigenstate preparation, it has yet to be implemented on an actual quantum device. In this work, we apply the rodeo algorithm to determine the energy levels of a random one-qubit Hamiltonian, resulting in a relative error of 0.08 % using mid-circuit measurements on the IBM Q device Casablanca. This surpasses the accuracy of directly-prepared eigenvector expectation values using the same quantum device. We take advantage of the high-accuracy energy determination and use the Hellmann–Feynman theorem to compute eigenvector expectation values for a different random one-qubit observable. For the Hellmann–Feynman calculations, we find a relative error of 0.7 % . We conclude by discussing possible future applications of the rodeo algorithm for multi-qubit Hamiltonians.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1140/epja/s10050-024-01373-9
