Benchmarking near-term quantum devices with the Variational Quantum Eigensolver and the Lipkin-Meshkov-Glick model

TL;DR

This paper benchmarks NISQ quantum devices using the Variational Quantum Eigensolver on the Lipkin-Meshkov-Glick model, demonstrating efficient circuit constructions for eigenstate preparation and validation against exact solutions.

Contribution

It introduces quantum circuits inspired by the LMG model's algebraic structure to efficiently prepare eigenstates for benchmarking NISQ devices.

Findings

Constructed circuits with depth O(N) and O(log N) for eigenstate preparation

Number of gates scales as O(N) for both circuit types

Eigenstate energies match exactly known solutions

Abstract

The Variational Quantum Eigensolver (VQE) 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. 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 $\mathcal{O}(\log_2N)$ 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.