论文标题
用随机参数移动规则测量一般量子演化的分析梯度
Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule
论文作者
论文摘要
杂交量子经典优化算法代表了近期量子计算机最有前途的应用之一。在这些算法中，目标是使用在量子设备上执行的测量结果来优化有关某些经典参数的可观察数量。在这里，我们研究了要直接从量子测量中优化的函数梯度的问题，从而概括并简化了文献中存在的某些方法，例如所谓的参数转移规则。我们得出了一种数学上精确的公式，该公式提供了一种随机算法，用于估计任何多量参数量子演化的梯度，而无需引入辅助量子尺寸或使用汉密尔顿模拟技术。当底层设备能够实现哈密顿量膨胀的所有Pauli旋转时，其系数取决于参数的所有Pauli旋转时，就可以进行梯度测量。尽管有一些近似值，即使所有可用的量子门都是嘈杂的，例如，由于量子设备和未知环境之间的耦合，我们的算法仍继续起作用。
Hybrid quantum-classical optimization algorithms represent one of the most promising application for near-term quantum computers. In these algorithms the goal is to optimize an observable quantity with respect to some classical parameters, using feedback from measurements performed on the quantum device. Here we study the problem of estimating the gradient of the function to be optimized directly from quantum measurements, generalizing and simplifying some approaches present in the literature, such as the so-called parameter-shift rule. We derive a mathematically exact formula that provides a stochastic algorithm for estimating the gradient of any multi-qubit parametric quantum evolution, without the introduction of ancillary qubits or the use of Hamiltonian simulation techniques. The gradient measurement is possible when the underlying device can realize all Pauli rotations in the expansion of the Hamiltonian whose coefficients depend on the parameter. Our algorithm continues to work, although with some approximations, even when all the available quantum gates are noisy, for instance due to the coupling between the quantum device and an unknown environment.
