Natural evolutionary strategies (NES) are a family of gradient-free black-box optimization algorithms. This study illustrates their use for the optimization of randomly initialized parameterized quantum circuits (PQCs) in the region of vanishing gradients. We show that using the NES gradient estimator the exponential decrease in variance can be alleviated. We implement two specific approaches, the exponential and separable NES, for parameter optimization of PQCs and compare them against standard gradient descent. We apply them to two different problems of ground state energy estimation using variational quantum eigensolver and state preparation with circuits of varying depth and length. We also introduce batch optimization for circuits with larger depth to extend the use of ES to a larger number of parameters. We achieve accuracy comparable to state-of-the-art optimization techniques in all the above cases with a lower number of circuit evaluations. Our empirical results indicate that one can use NES as a hybrid tool in tandem with other gradient-based methods for optimization of deep quantum circuits in regions with vanishing gradients.

自然进化策略 (NES) 是一系列无梯度黑盒优化算法。这项研究说明了它们在梯度消失区域中优化随机初始化参数化量子电路 (PQC) 的用途。我们表明，使用 NES 梯度估计器可以缓解方差的指数下降。我们实现了两种特定方法，指数和可分离 NES，用于 PQC 的参数优化，并将它们与标准梯度下降进行比较。我们将它们应用于使用变分量子本征求解器和具有不同深度和长度的电路的状态准备的基态能量估计的两个不同问题。我们还为具有更大深度的电路引入了批量优化，以将 ES 的使用扩展到更多参数。在上述所有情况下，我们以较少的电路评估次数实现了与最先进的优化技术相当的精度。我们的实证结果表明，可以将 NES 作为一种混合工具与其他基于梯度的方法结合使用，以优化梯度消失区域中的深量子电路。