Benchmarking VQE with the LMG model
Kenneth C. Robbins, Peter J. Love · arXiv (Cornell University) · 2021
The Variational Quantum Eigensolver (VQE) is a promising algorithm for Noisy Intermediate-Scale Quantum (NISQ) computation. Verification and validation of NISQ algorithms is an important task. We consider the exactly-diagonalizable Lipkin-Meshkov-Glick (LMG) model as a candidate for benchmarking. We can 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 $O(N)$ and $O(\log_2 N)$ that can prepare any trigonometric LMG eigenstate of $N$ particles. The number of gates required for both circuits is $O(N)$.