Efficient Online Quantum Circuit Learning with No Upfront Training

We propose a surrogate-based method for optimizing parameterized quantum circuits which is designed to operate with few calls to a quantum computer. We employ a computationally inexpensive classical surrogate to approximate the cost function of a variational quantum algorithm. An initial surrogate is fit to data obtained by sparse sampling of the true cost function using noisy quantum computers. The surrogate is iteratively refined by querying the true cost at the surrogate optima, then using radial basis function interpolation with existing and new true cost data. The use of radial basis function interpolation enables surrogate construction without hyperparameters to pre-train. Additionally, using the surrogate as an acquisition function focuses hardware queries in the vicinity of the true optima. For 16-qubit random 3-regular Max-Cut problems solved using the QAOA ansatz, we find that our method outperforms the prior state of the art. Furthermore, we demonstrate successful optimization of QAOA circuits for 127-qubit random Ising models on an IBM quantum processor using measurement counts of the order of $10^4-10^5$. The strong empirical performance of this approach is an important step towards the large-scale practical application of variational quantum algorithms and a clear demonstration of the effectiveness of classical-surrogate-based learning approaches.