Benchmarking near-term quantum devices with the variational quantum eigensolver and the Lipkin-Meshkov-Glick model

Robbins, Kenneth; Love, Peter J.

doi:10.1103/physreva.104.022412

Title: Benchmarking near-term quantum devices with the variational quantum eigensolver and the Lipkin-Meshkov-Glick model

Abstract

The variational quantum eigensolver is a promising algorithm for noisy intermediate scale quantum (NISQ) computation. Verification and validation of NISQ algorithms' performance on NISQ devices is an important task. Here, we consider the exactly diagonalizable Lipkin-Meshkov-Glick (LMG) model as a candidate for benchmarking NISQ computers. We use the Bethe Ansatz to construct eigenstates of the trigonometric LMG model using quantum circuits inspired by the LMG's underlying algebraic structure. We construct circuits with depth $$\mathcal{O}$$(N) and $$\mathcal{O}$$(log₂N) that can prepare any trigonometric LMG eigenstate of N particles. The number of gates required for both circuits is $$\mathcal{O}$$(N). The energies of the eigenstates can then be measured and compared to the exactly known answers.

Authors:

^[1]; Love, Peter J. ^[2]

Tufts Univ., Medford, MA (United States)
Tufts Univ., Medford, MA (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)

Publication Date:: Mon Aug 16 00:00:00 EDT 2021

Research Org.:: Univ. of Wisconsin, Madison, WI (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1830660

Alternate Identifier(s):: OSTI ID: 1870305

Grant/Contract Number:: SC0019465

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review A

Additional Journal Information:: Journal Volume: 104; Journal Issue: 2; Journal ID: ISSN 2469-9926

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 97 MATHEMATICS AND COMPUTING; Quantum algorithms; Quantum computation

Citation Formats


                    Robbins, Kenneth, and Love, Peter J. Benchmarking near-term quantum devices with the variational quantum eigensolver and the Lipkin-Meshkov-Glick model.  United States: N. p., 2021. 
Web.  doi:10.1103/physreva.104.022412.

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                    Robbins, Kenneth, & Love, Peter J. Benchmarking near-term quantum devices with the variational quantum eigensolver and the Lipkin-Meshkov-Glick model.  United States.  https://doi.org/10.1103/physreva.104.022412

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                    Robbins, Kenneth, and Love, Peter J. Mon .  
"Benchmarking near-term quantum devices with the variational quantum eigensolver and the Lipkin-Meshkov-Glick model".  United States.  https://doi.org/10.1103/physreva.104.022412.  https://www.osti.gov/servlets/purl/1830660.

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@article{osti_1830660,

  title        = {Benchmarking near-term quantum devices with the variational quantum eigensolver and the Lipkin-Meshkov-Glick model},

  author       = {Robbins, Kenneth and Love, Peter J.},

  abstractNote = {The variational quantum eigensolver is a promising algorithm for noisy intermediate scale quantum (NISQ) computation. Verification and validation of NISQ algorithms' performance on NISQ devices is an important task. Here, we consider the exactly diagonalizable Lipkin-Meshkov-Glick (LMG) model as a candidate for benchmarking NISQ computers. We use the Bethe Ansatz to construct eigenstates of the trigonometric LMG model using quantum circuits inspired by the LMG's underlying algebraic structure. We construct circuits with depth $\mathcal{O}$(N) and $\mathcal{O}$(log2N) that can prepare any trigonometric LMG eigenstate of N particles. The number of gates required for both circuits is $\mathcal{O}$(N). The energies of the eigenstates can then be measured and compared to the exactly known answers.},

  doi          = {10.1103/physreva.104.022412},

  journal      = {Physical Review A},

  number       = 2,

  volume       = 104,

  place        = {United States},

  year         = {Mon Aug 16 00:00:00 EDT 2021},

  month        = {Mon Aug 16 00:00:00 EDT 2021}

}

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Title: Benchmarking near-term quantum devices with the variational quantum eigensolver and the Lipkin-Meshkov-Glick model

Abstract

Citation Formats

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A Derivation of n-Dimensional Spherical Coordinates journal, January 1960

Quantum Computing in the NISQ era and beyond journal, August 2018

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Kitaev honeycomb tensor networks: Exact unitary circuits and applications journal, January 2017

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