We present and analyze large-scale simulation results of a hybrid quantum-classical variational method to calculate the ground state energy of the anti-ferromagnetic Heisenberg model. Using a massively parallel universal quantum computer simulator, we observe that a low-depth-circuit ansatz advantageously exploits the efficiently preparable N\'{e}el initial state, avoids potential barren plateaus, and works for both one- and two-dimensional lattices. The analysis reflects the decisive ingredients required for a simulation by comparing different ans\"{a}tze, initial parameters, and gradient-based versus gradient-free optimizers. Extrapolation to the thermodynamic limit accurately yields the analytical value for the ground state energy, given by the Bethe ansatz. We predict that a fully functional quantum computer with 100 qubits can calculate the ground state energy with a relatively small error.
@article{arxiv.2201.05065,
title = {Assessment of the variational quantum eigensolver: application to the Heisenberg model},
author = {Manpreet Singh Jattana and Fengping Jin and Hans De Raedt and Kristel Michielsen},
journal= {arXiv preprint arXiv:2201.05065},
year = {2022}
}