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

Journal Article · 16 August 2021 · Physical Review A

DOI: https://doi.org/10.1103/physreva.104.022412 · OSTI ID:1830660

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

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1. Tufts Univ., Medford, MA (United States); University of Wisconsin, Madison
2. Tufts Univ., Medford, MA (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)

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.

• Research Organization: Univ. of Wisconsin, Madison, WI (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0019465
• OSTI ID: 1830660
• Journal Information: Physical Review A, Journal Name: Physical Review A Journal Issue: 2 Vol. 104; ISSN 2469-9926
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English