Variational Monte Carlo and the Quantum Enhanced Metropolis-Hastings Algorithm

This work explores the adaptation of the classical Metropolis-Hastings algorithm into a quantum-enhanced framework to improve sampling efficiency in variational Monte Carlo. Utilizing variational Monte Carlo, and in particular the single thread Monte Carlo method, we estimate the dominant eigenvalue of a symmetric 3 × 3 matrix which could represent the ground state energy of a three-level quantum system. We compare classical and hybrid quantum-classical implementations, where the latter employs the quantum enhanced Metropolis-Hastings algorithm. It is shown that the hybrid version demonstrates accelerated convergence and higher precision in a simulated environment.