论文标题
量子分类器的转移学习：信息理论泛化分析
Transfer Learning for Quantum Classifiers: An Information-Theoretic Generalization Analysis
论文作者
论文摘要
在经典输入上运行的量子机学习模型的关键组成部分是将嵌入电路映射输入到量子状态的设计。本文研究了传输学习设置，其中通过任意参数量子电路进行经典到量词嵌入，该量子是根据源任务的数据进行预训练的。在运行时，嵌入的二进制量子分类器根据目标任务的数据进行了优化。由此产生的分类器的平均多余风险，即最佳差距，取决于（dis）相似的源和目标任务。我们通过痕量距离引入了二进制量子分类任务之间（DIS）相似性的新度量。最佳差距上的上限是根据提议的任务（DIS）相似性度量得出的，在源和目标任务下经典输入和量子嵌入之间的两个r $é$ nyi相互信息术语，以及在源任务下的量子嵌入式和分类器组合空间的复杂度的量度。理论结果在一个简单的二进制分类示例中得到了验证。
A key component of a quantum machine learning model operating on classical inputs is the design of an embedding circuit mapping inputs to a quantum state. This paper studies a transfer learning setting in which classical-to-quantum embedding is carried out by an arbitrary parametric quantum circuit that is pre-trained based on data from a source task. At run time, a binary quantum classifier of the embedding is optimized based on data from the target task of interest. The average excess risk, i.e., the optimality gap, of the resulting classifier depends on how (dis)similar the source and target tasks are. We introduce a new measure of (dis)similarity between the binary quantum classification tasks via the trace distances. An upper bound on the optimality gap is derived in terms of the proposed task (dis)similarity measure, two R$é$nyi mutual information terms between classical input and quantum embedding under source and target tasks, as well as a measure of complexity of the combined space of quantum embeddings and classifiers under the source task. The theoretical results are validated on a simple binary classification example.
