A key step in quantum machine learning with 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, the binary classifier is then optimized based on data from the target task of interest. Using an information-theoretic approach, we demonstrate that the average excess risk, or optimality gap, can be bounded in terms of two R\'enyi mutual information terms between classical input and quantum embedding under source and target tasks, as well as in terms of a measure of similarity between the source and target tasks related to the trace distance. The main theoretical results are validated on a simple binary classification example.
翻译:使用古典投入的量子机器学习的一个关键步骤是设计一个嵌入到量子状态的电路绘图输入。 本文研究一个传输学习环境, 传统到量子嵌入由根据来源任务的数据预先培训的任意参数量子电路进行。 运行时, 二进制分类器随后根据目标利益任务的数据优化。 使用信息理论方法, 我们证明, 平均超额风险或最佳性差距可以以两个R' enyi相互信息条件为界限, 即传统输入和量子嵌入源和目标任务之间的两个R' enyi信息条件为界限, 以及源和目标任务与跟踪距离相关任务之间的类似性衡量标准。 主要理论结果通过简单的二进制分类示例验证。