An Exactly-Solvable Model as a Benchmark for VQE

The Noisy Intermediate-Scale Quantum (NISQ) era of computation provides new opportunities for calculations with the Variational Quantum Eigensolver (VQE) algorithm but these machines will require benchmarking. The Lipkin-Meshkov-Glick (LMG) model provides an exact standard for which to compare the results of VQE. By exploiting the algebraic structure of the LMG Hamiltonian we use the Bethe ansatz to design a state-preparation quantum circuit to generate ansatz states for the LMG. The proposed circuit is qudit-based and scales to simulate higher numbers of particles.