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Quantum techniques for eigenvalue problems

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A Publisher Erratum to this article was published on 30 January 2024

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Abstract

This article is a brief introduction to quantum algorithms for the eigenvalue problem in quantum many-body systems. Rather than a broad survey of topics, we focus on providing a conceptual understanding of several quantum algorithms that cover the essentials of adiabatic evolution, variational methods, phase detection algorithms, and several other approaches. For each method, we discuss the potential advantages and remaining challenges.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This article describes algorithms with derivations, and all information needed to reproduce the work is contained within the article itself.]

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Acknowledgements

The author acknowledges support from the U.S. National Science Foundation (PHY-2310620), U.S. Department of Energy (DE-SC0021152, DE-SC0013365, DE-SC0023658) and the SciDAC-4 and SciDAC-5 NUCLEI Collaborations. This research used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725.

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  1. Facility for Rare Isotope Beams and Department of Physics and Astronomy, Michigan State University, East Lansing, MI, 48824, USA

    Dean Lee

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Communicated by Thomas Duguet.

The original online version of this article was revised: The equation “\(e^A e^B = e^C\)” in the preceding sentence, just before Eq. (6), was inaccurately presented.

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Lee, D. Quantum techniques for eigenvalue problems. Eur. Phys. J. A 59, 275 (2023). https://doi.org/10.1140/epja/s10050-023-01183-5

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