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Variational quantum algorithms are a leading candidate for early applicationson noisy intermediate-scale quantum computers. These algorithms depend on aclassical optimization outer-loop that minimizes some function of aparameterized quantum circuit. In practice, finite sampling error and gateerrors make this a stochastic optimization with unique challenges that must beaddressed at the level of the optimizer. The sharp trade-off between precisionand sampling time in conjunction with experimental constraints necessitates thedevelopment of new optimization strategies to minimize overall wall clock timein this setting. In this work, we introduce two optimization methods andnumerically compare their performance with common methods in use today. Themethods are surrogate model-based algorithms designed to improve reuse ofcollected data. They do so by utilizing a least-squares quadratic fit ofsampled function values within a moving trusted region to estimate the gradientor a policy gradient. To make fair comparisons between optimization methods, wedevelop experimentally relevant cost models designed to balance efficiency intesting and accuracy with respect to cloud quantum computing systems. Theresults here underscore the need to both use relevant cost models and optimizehyperparameters of existing optimization methods for competitive performance.The methods introduced here have several practical advantages in realisticexperimental settings, and we have used one of them successfully in aseparately published experiment on Google's Sycamore device.

Using models to improve optimizers for variational quantum algorithms