Variational Monte Carlo and the Quantum Enhanced Metropolis-Hastings Algorithm

Abstract This work explores adapting 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 $$\times $$ × 3 matrix, serving as the toy model for 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. In a simulated environment, the hybrid version demonstrates faster convergence and improved estimator precision for this test case.