反向地图投影作为等变量子嵌入
Reverse Map Projections as Equivariant Quantum Embeddings
AI总结：
本文提出一类新的反向地图投影嵌入，用于将经典数据编码为量子态，解决振幅嵌入丢失范数信息的问题，并作为等变嵌入提升量子机器学习性能，实验表明其优于标准振幅嵌入。
摘要：
我们引入了一类新的反向地图投影嵌入$(E_α)_{α\in [-\infty,1)}$，每种嵌入都定义了一种将经典数据编码为量子态的新方法。受制图学中实际使用的从单位球面到其切平面的著名地图投影的启发，这些嵌入解决了振幅嵌入方法的常见缺点，即数据点的标量倍数被识别，导致数据范数信息丢失。我们展示了如何将反向地图投影用作量子机器学习中的等变嵌入。利用这些方法，我们可以利用经典数据集中的对称性来显著增强量子机器学习任务的性能。最后，我们选择四个$α$值执行一个简单的分类任务，以$E_α$作为嵌入，并同时实验等变和非等变设置。我们将它们的结果与标准振幅嵌入的结果进行比较。
英文摘要：
We introduce the novel class $(E_α)_{α\in [-\infty,1)}$ of reverse map projection embeddings, each one defining a unique new method of encoding classical data into quantum states. Inspired by well-known map projections from the unit sphere onto its tangent planes, used in practice in cartography, these embeddings address the common drawback of the amplitude embedding method, wherein scalar multiples of data points are identified and information about the norm of data is lost. We show how reverse map projections can be utilised as equivariant embeddings for quantum machine learning. Using these methods, we can leverage symmetries in classical datasets to significantly strengthen performance on quantum machine learning tasks. Finally, we select four values of $α$ with which to perform a simple classification task, taking $E_α$ as the embedding and experimenting with both equivariant and non-equivariant setups. We compare their results alongside those of standard amplitude embedding.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
