Noise-induced transition in optimal solutions of variational quantum algorithms

Variational quantum algorithms are widely considered a promising class of near-team algorithms that may demonstrate a practical quantum advantage in problems of scientific interest. One of the major obstacles to a scalable realization is the difficulty in optimizing the noisy cost function. In this work, we investigate the effect of noise on the optimization. By studying a simple model, we observe an abrupt transition induced by noise to the optimal solution. We will present the numerical simulation, experimental demonstration using IBM QPUs, and theoretical analysis indicating that similar transitions exist beyond the simple model. Our results suggest that a careful examination of the optimal solutions is necessary to ensure the qualitative correctness of the solutions when implementing variational algorithms on NISQ hardware.