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Optimizing parameterized quantum circuits is a key routine in using near-termquantum devices. However, the existing algorithms for such optimization requirean excessive number of quantum-measurement shots for estimating expectationvalues of observables and repeating many iterations, whose cost has been acritical obstacle for practical use. We develop an efficient alternativeoptimization algorithm, stochastic gradient line Bayesian optimization (SGLBO),to address this problem. SGLBO reduces the measurement-shot cost by estimatingan appropriate direction of updating circuit parameters based on stochasticgradient descent (SGD) and further utilizing Bayesian optimization (BO) toestimate the optimal step size for each iteration in SGD. In addition, weformulate an adaptive measurement-shot strategy and introduce a technique ofsuffix averaging to reduce the effect of statistical and hardware noise. Ournumerical simulation demonstrates that the SGLBO augmented with thesetechniques can drastically reduce the measurement-shot cost, improve theaccuracy, and make the optimization noise-robust.

Stochastic Gradient Line Bayesian Optimization for Efficient Noise-Robust Optimization of Parameterized Quantum Circuits