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arXiv 2008.06517quant-ph
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在量子硬件上估计梯度和高阶导数

Estimating the gradient and higher-order derivatives on quantum hardware

Andrea Mari, Thomas R. Bromley, Nathan Killoran

备注：
Source code for the numerics in this paper can be found at https://github.com/XanaduAI/derivatives-of-variational-circuits (v2) updated Fubini-Study metric definition and corrected typo in resulting equations
发表信息：
Phys. Rev. A 103, 012405 (2021)
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摘要：

对于一个大类的变分量子线路，我们显示了如何任意阶导数可以分析评估在简单的参数移位规则，即，通过以不同的参数偏移运行相同的电路。作为特殊情况下，我们得到的期望值的海森和变分状态的度量张量，这两者都可以有效地用于分析实现二阶优化算法的量子计算机上的参数移位规则。我们还考虑统计噪声的影响，通过研究不同的导数估计的均方误差。在这项工作的第二部分，一些用于评估量子导数的理论技术被应用于它们的典型用例：量子优化器的实现。我们发现，不同的估计器和优化器的性能与不同的超参数的值交织在一起，例如步长或拍摄次数。我们的研究结果支持几个数值和硬件实验，包括一个简单的变分电路和牛顿优化器的实现的海森的实验估计。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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