  Hybrid quantum-classical optimization using near-term quantum technology is
an emerging direction for exploring quantum advantage in high-dimensional
systems. However, precise characterization of all experimental parameters is
often impractical and challenging. A viable approach is to use algorithms that
rely only on black-box inference rather than analytical gradients. Here, we
combine randomized perturbation gradient estimation with adaptive momentum
gradient updates to create the AdamSPSA and AdamRSGF algorithms. We prove the
asymptotic convergence of our algorithms in a convex setting, and we benchmark
them against other gradient-based optimization algorithms on non-convex optimal
control tasks. Our results show that these new algorithms accelerate the
convergence rate, decrease the variance of loss trajectories, and efficiently
tune up high-fidelity (above 99.9\%) Hann-window single-qubit gates from
trivial initial conditions with twenty variables.
