Variational Monte Carlo with Conditional-Value-at-Risk Objective Function

Previous work by Barkoutsos et. al has shown that the convergence of quantum optimization algorithms can be greatly improved by replacing the usual expectation of the Hamiltonian operator with the Conditional-Value-at-Risk (CVar). However, empirical results were only demonstrated on small problem sizes due to limited simulation resources. We propose to simulate the behavior of quantum approximate optimization algorithms for large problem sizes with Variational Monte Carlo, which displays similar theoretical properties with quantum optimization algorithms. We verified that using CVar as the objective function, which considers only a subset of samples queried from the quantum state, generally improves the rate of convergence as well as the quality of the result. Yet, the size of the subset included in the calculation must be treated as an additional hyperparameter and be chosen carefully to ensure maximal performance.