Qubit control protocols have traditionally leveraged a characterisation of the qubit-bath coupling via its power spectral density. Previous work proposed the inference of noise operators that characterise the influence of a classical bath using a grey-box approach that combines deep neural networks with physics-encoded layers. This overall structure is complex and poses challenges in scaling and real-time operations. Here, we show that no expensive neural networks are needed and that this noise operator description admits an efficient parameterisation. We refer to the resulting parameter space as the \textit{quantum feature space} of the qubit dynamics resulting from the coupled bath. We show that the Euclidean distance defined over the quantum feature space provides an effective method for classifying noise processes in the presence of a given set of controls. Using the quantum feature space as the input space for a simple machine learning algorithm (random forest, in this case), we demonstrate that it can effectively classify the stationarity and the broad class of noise processes perturbing a qubit. Finally, we explore how control pulse parameters map to the quantum feature space.

翻译：量子比特控制协议传统上通过功率谱密度来表征量子比特-浴耦合。先前的研究提出了一种灰盒方法，将深度神经网络与物理编码层相结合，用于推断表征经典浴影响的噪声算符。该整体结构复杂，在可扩展性和实时操作方面面临挑战。本文证明，无需昂贵的神经网络，且该噪声算符描述允许一种高效的参数化。我们将由此产生的参数空间称为由耦合浴引起的量子比特动力学的量子特征空间。我们证明，在量子特征空间上定义的欧几里得距离为在给定控制集存在下对噪声过程进行分类提供了一种有效方法。使用量子特征空间作为简单机器学习算法（本文中为随机森林）的输入空间，我们证明其能有效分类扰动量子比特的噪声过程的平稳性及大类。最后，我们探讨了控制脉冲参数如何映射到量子特征空间。