Convergence of SPSA-based VQE for the 3x4 Fermi-Hubbard lattice at U=0

Determine whether the Simultaneous Perturbation Stochastic Approximation optimizer within the variational quantum eigensolver, applied to the 3x4 half-filled Fermi-Hubbard lattice with on-site interaction U=0, converges to the classically computed ground-state energy E_g = -16.6 when granted sufficient runtime and computing resources.

Background

The paper applies a variational quantum eigensolver (VQE) with an SPSA classical optimizer to compute ground-state energies of the Fermi-Hubbard model on small lattices. While results for 1x4, 2x2, and 2x4 lattices show close agreement with classical calculations, scaling to a 3x4 lattice introduces substantial computational demands.

For the 3x4 U=0 case, the authors report partial optimization progress but were constrained by a 72-hour job limit and the large number of parameters in the ansatz. They observed convergence behavior trending toward the true energy but could not complete runs long enough to confirm the final outcome. This leaves unresolved whether the SPSA optimizer would reach the true ground-state energy given adequate time and resources.