Large-scale comparison of PPE-based sampling with VQE optimizers

Conduct a competitive, large-scale comparison of the Poisson product estimator coupled with simulated annealing against gradient-based and gradient-free variational quantum eigensolver optimizers, including simultaneous perturbation stochastic approximation.

Background

The paper introduces the Poisson product estimator (PPE), an unbiased and non-negative estimator of Boltzmann weights when energies are available only through stochastic estimates. Coupled with simulated annealing, the PPE provides a gradient-free approach to minimizing variational quantum-circuit energies and is demonstrated on the H₃⁺ molecule in a minimal basis.

The authors note that their demonstration does not provide a competitive, large-scale benchmark against established variational quantum eigensolver (VQE) optimization methods. Such a comparison would assess the practical performance of PPE-based sampling relative to both gradient-based methods and gradient-free methods such as simultaneous perturbation stochastic approximation.