Efficient Algorithms for High-Dimensional Quantum Optimal Control of a Transmon Qubit

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 entirely on black-box inference rather than analytical gradients. Here, we combine randomized perturbation gradient estimation with adaptive momentum gradient updates and propose AdamSPSA and AdamRSGF algorithms. We prove the asymptotic convergence of the proposed algorithms in a convex setting and benchmark them against other gradient-based black-box optimization algorithms on nonconvex quantum optimal control tasks. Our results indicate that these algorithms accelerate the optimization rate, lower the optimization loss, and efficiently tune up high-fidelity Hann-window single-qubit gates from trivial initial conditions with up to 80 variables for a transmon qubit.