  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.
