  Optimizing parameterized quantum circuits is a key routine in using near-term
quantum devices. However, the existing algorithms for such optimization require
an excessive number of quantum-measurement shots for estimating expectation
values of observables and repeating many iterations, whose cost has been a
critical obstacle for practical use. We develop an efficient alternative
optimization algorithm, stochastic gradient line Bayesian optimization (SGLBO),
to address this problem. SGLBO reduces the measurement-shot cost by estimating
an appropriate direction of updating circuit parameters based on stochastic
gradient descent (SGD) and further utilizing Bayesian optimization (BO) to
estimate the optimal step size for each iteration in SGD. In addition, we
formulate an adaptive measurement-shot strategy and introduce a technique of
suffix averaging to reduce the effect of statistical and hardware noise. Our
numerical simulation demonstrates that the SGLBO augmented with these
techniques can drastically reduce the measurement-shot cost, improve the
accuracy, and make the optimization noise-robust.
