用师生方案探索量子感知器和量子神经网络结构
Exploring Quantum Perceptron and Quantum Neural Network structures with a teacher-student scheme
摘要：
近期量子设备可用于构建量子机器学习模型，例如量子核方法和量子神经网络（QNN）来执行分类任务。如何将变分量子线路用作量子感知器或量子神经网络已经有许多建议。这项工作的目的是系统地比较不同的QNN架构，并评估他们的相对表达能力与师生计划。具体来说，教师模型生成将随机输入映射到输出的数据集，然后学生模型必须学习这些数据集。通过这种方式，我们避免了在任意数据集上进行训练，并允许直接通过损失，预测图，准确性和预测图之间的相对熵来比较不同模型的学习能力。我们特别关注的量子感知器模型的启发，最近的工作Tacchino等。\cite{Tacchino1}，并将其与最初由Pérez-Salinas et. \cite{data_re-uploading} .我们讨论了感知器模型的改变和深度QNN的形成，以更好地理解隐藏单元和非线性在这些架构中的作用。
英文摘要：
Near-term quantum devices can be used to build quantum machine learning models, such as quantum kernel methods and quantum neural networks (QNN) to perform classification tasks. There have been many proposals how to use variational quantum circuits as quantum perceptrons or as QNNs. The aim of this work is to systematically compare different QNN architectures and to evaluate their relative expressive power with a teacher-student scheme. Specifically, the teacher model generates the datasets mapping random inputs to outputs which then have to be learned by the student models. This way, we avoid training on arbitrary data sets and allow to compare the learning capacity of different models directly via the loss, the prediction map, the accuracy and the relative entropy between the prediction maps. We focus particularly on a quantum perceptron model inspired by the recent work of Tacchino et. al. \cite{Tacchino1} and compare it to the data re-uploading scheme that was originally introduced by Pérez-Salinas et. al. \cite{data_re-uploading}. We discuss alterations of the perceptron model and the formation of deep QNN to better understand the role of hidden units and non-linearities in these architectures.
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