Quantum-enhanced data science, also known as quantum machine learning (QML), is of growing interest as an application of near-term quantum computers. Variational QML algorithms have the potential to solve practical problems on real hardware, particularly when involving quantum data. However, training these algorithms can be challenging and calls for tailored optimization procedures. Specifically, QML applications can require a large shot-count overhead due to the large datasets involved. In this work, we advocate for simultaneous random sampling over both the dataset as well as the measurement operators that define the loss function. We consider a highly general loss function that encompasses many QML applications, and we show how to construct an unbiased estimator of its gradient. This allows us to propose a shot-frugal gradient descent optimizer called Refoqus (REsource Frugal Optimizer for QUantum Stochastic gradient descent). Our numerics indicate that Refoqus can save several orders of magnitude in shot cost, even relative to optimizers that sample over measurement operators alone.

翻译：量子增强数据科学，又称量子机器学习（QML），作为近期量子计算机的应用正日益受到关注。变分QML算法在解决实际硬件上的实际问题方面具有潜力，尤其是在涉及量子数据时。然而，训练这些算法可能具有挑战性，需要定制的优化程序。具体而言，QML应用可能由于涉及大规模数据集而导致巨大的测量次数开销。在这项工作中，我们主张同时对数据集和定义损失函数的测量算子进行随机采样。我们考虑了一个高度通用的损失函数，涵盖了众多QML应用，并展示了如何构建其梯度的无偏估计量。由此，我们提出了一种节俭测量次数的梯度下降优化器，名为Refoqus（面向量子随机梯度下降的资源节俭优化器）。我们的数值结果表明，即便与仅对测量算子进行采样的优化器相比，Refoqus也能节省数个数量级的测量次数成本。