论文标题
量子分类器的强大数据编码
Robust data encodings for quantum classifiers
论文作者
论文摘要
数据表示对于机器学习模型的成功至关重要。在使用近期量子计算机的量子机学习的背景下，同样重要的考虑如何有效输入（编码）数据并有效地处理噪声。在这项工作中，我们研究了用于二进制量子分类的数据编码，并在有和没有噪声的情况下研究它们的性质。对于我们考虑的共同分类器，我们表明编码确定可学习的决策边界的类别以及在存在噪声的情况下保留相同分类的点集。在定义了鲁棒数据编码的概念之后，我们证明了有关不同通道的鲁棒性的几个结果，讨论了健壮的编码的存在，并证明了在嘈杂和无噪声状态之间的忠诚度方面对可靠点的上限进行了界限。提供了几种示例实现的数值结果，以加强我们的发现。
Data representation is crucial for the success of machine learning models. In the context of quantum machine learning with near-term quantum computers, equally important considerations of how to efficiently input (encode) data and effectively deal with noise arise. In this work, we study data encodings for binary quantum classification and investigate their properties both with and without noise. For the common classifier we consider, we show that encodings determine the classes of learnable decision boundaries as well as the set of points which retain the same classification in the presence of noise. After defining the notion of a robust data encoding, we prove several results on robustness for different channels, discuss the existence of robust encodings, and prove an upper bound on the number of robust points in terms of fidelities between noisy and noiseless states. Numerical results for several example implementations are provided to reinforce our findings.
