论文标题
估计量子硬件上的梯度和高阶导数
Estimating the gradient and higher-order derivatives on quantum hardware
论文作者
论文摘要
对于一大批变异量子电路，我们展示了如何通过运行具有不同参数偏移的相同电路来通过简单的参数迁移规则来分析任意阶数。作为特定情况，我们获得了期望值的Hessian的参数切换规则以及各种状态的度量张量，这两者都可以有效地用于分析量子计算机上的二阶优化算法。我们还通过研究不同导数估计量的平方误差来考虑统计噪声的影响。在这项工作的第二部分中，将一些用于评估量子衍生物的理论技术应用于其典型用例：量子优化器的实现。我们发现，不同估计器和优化器的性能与不同的超参数的值（例如步长或许多镜头）交织在一起。我们的发现得到了几个数值和硬件实验的支持，包括对简单变分路的Hessian的实验估计以及牛顿优化器的实现。
For a large class of variational quantum circuits, we show how arbitrary-order derivatives can be analytically evaluated in terms of simple parameter-shift rules, i.e., by running the same circuit with different shifts of the parameters. As particular cases, we obtain parameter-shift rules for the Hessian of an expectation value and for the metric tensor of a variational state, both of which can be efficiently used to analytically implement second-order optimization algorithms on a quantum computer. We also consider the impact of statistical noise by studying the mean squared error of different derivative estimators. In the second part of this work, some of the theoretical techniques for evaluating quantum derivatives are applied to their typical use case: the implementation of quantum optimizers. We find that the performance of different estimators and optimizers is intertwined with the values of different hyperparameters, such as a step size or a number of shots. Our findings are supported by several numerical and hardware experiments, including an experimental estimation of the Hessian of a simple variational circuit and an implementation of the Newton optimizer.
