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Variational quantum algorithms rely on the optimization of parameterizedquantum circuits in noisy settings. The commonly used back-propagationprocedure in classical machine learning is not directly applicable in thissetting due to the collapse of quantum states after measurements. Thus,gradient estimations constitute a significant overhead in a gradient-basedoptimization of such quantum circuits. This paper introduces a randomcoordinate descent algorithm as a practical and easy-to-implement alternativeto the full gradient descent algorithm. This algorithm only requires onepartial derivative at each iteration. Motivated by the behavior of measurementnoise in the practical optimization of parameterized quantum circuits, thispaper presents an optimization problem setting that is amenable to analysis.Under this setting, the random coordinate descent algorithm exhibits the samelevel of stochastic stability as the full gradient approach, making it asresilient to noise. The complexity of the random coordinate descent method isgenerally no worse than that of the gradient descent and can be much better forvarious quantum optimization problems with anisotropic Lipschitz constants.Theoretical analysis and extensive numerical experiments validate our findings.

Random coordinate descent: a simple alternative for optimizing parameterized quantum circuits