论文标题
用于机器学习的量子嵌入
Quantum embeddings for machine learning
论文作者
论文摘要
量子分类器是可训练的量子电路，用作机器学习模型。电路的第一部分实现了将经典输入编码到量子状态的量子特征图，将数据嵌入高维的希尔伯特空间中；电路的第二部分执行了解释为模型输出的量子测量。通常，对测量进行训练以区分量子包裹的数据。我们建议改为训练电路的第一部分 - 嵌入 - 目的是将希尔伯特空间中的数据类别分开，这是我们称为量子公制的策略。结果，测量最小化线性分类损失的测量已知，并取决于所使用的度量：对于使用L1或痕量距离分离数据的嵌入，这是Helstrom测量值，而对于L2或Hilbert-Schmidt距离，这是一个简单的重叠测量。这种方法为量子机学习提供了一个强大的分析框架，并消除了当前模型中的主要组成部分，从而释放了更多宝贵的资源，以最好地利用近期量子信息处理器的功能。
Quantum classifiers are trainable quantum circuits used as machine learning models. The first part of the circuit implements a quantum feature map that encodes classical inputs into quantum states, embedding the data in a high-dimensional Hilbert space; the second part of the circuit executes a quantum measurement interpreted as the output of the model. Usually, the measurement is trained to distinguish quantum-embedded data. We propose to instead train the first part of the circuit -- the embedding -- with the objective of maximally separating data classes in Hilbert space, a strategy we call quantum metric learning. As a result, the measurement minimizing a linear classification loss is already known and depends on the metric used: for embeddings separating data using the l1 or trace distance, this is the Helstrom measurement, while for the l2 or Hilbert-Schmidt distance, it is a simple overlap measurement. This approach provides a powerful analytic framework for quantum machine learning and eliminates a major component in current models, freeing up more precious resources to best leverage the capabilities of near-term quantum information processors.
