论文标题
具有经典实例和量子标签的二进制分类
Binary Classification with Classical Instances and Quantum Labels
论文作者
论文摘要
在经典的统计学习理论中，研究最精心的问题之一是二进制分类。该任务的信息理论样本复杂性的紧密特征是Vapnik-Chervonenkis（VC）维度。对此任务的量子类似物，并且对量子状态给出的训练数据也进行了深入研究，现在众所周知，其样品复杂性与经典对应物具有相同的样本复杂性。 我们通过考虑具有经典输入和量子输出以及相应的经典量子训练数据的地图，提出了一个新颖的经典二进制分类任务的量子版本。我们讨论了不可知论者和可实现的情况的学习策略，并研究其性能以获得样本复杂性上限。此外，我们提供样品复杂性下限，表明我们的上限对于纯输出状态基本紧密。特别是，我们看到样本复杂性与经典二进制分类任务W.R.T.相同。它对准确性，信心和VC维度的依赖。
In classical statistical learning theory, one of the most well studied problems is that of binary classification. The information-theoretic sample complexity of this task is tightly characterized by the Vapnik-Chervonenkis (VC) dimension. A quantum analog of this task, with training data given as a quantum state has also been intensely studied and is now known to have the same sample complexity as its classical counterpart. We propose a novel quantum version of the classical binary classification task by considering maps with classical input and quantum output and corresponding classical-quantum training data. We discuss learning strategies for the agnostic and for the realizable case and study their performance to obtain sample complexity upper bounds. Moreover, we provide sample complexity lower bounds which show that our upper bounds are essentially tight for pure output states. In particular, we see that the sample complexity is the same as in the classical binary classification task w.r.t. its dependence on accuracy, confidence and the VC-dimension.
