The ability to extract general laws from a few known examples depends on the complexity of the problem and on the amount of training data. In the quantum setting, the learner's generalization performance is further challenged by the destructive nature of quantum measurements that, together with the no-cloning theorem, limits the amount of information that can be extracted from each training sample. In this paper we focus on hybrid quantum learning techniques where classical machine-learning methods are paired with quantum algorithms and show that, in some settings, the uncertainty coming from a few measurement shots can be the dominant source of errors. We identify an instance of this possibly general issue by focusing on the classification of maximally entangled vs. separable states, showing that this toy problem becomes challenging for learners unaware of entanglement theory. Finally, we introduce an estimator based on classical shadows that performs better in the big data, few copy regime. Our results show that the naive application of classical machine-learning methods to the quantum setting is problematic, and that a better theoretical foundation of quantum learning is required.

翻译：从少量已知示例中提取一般规律的能力取决于问题的复杂性和训练数据的数量。在量子场景中，学习器的泛化性能进一步受到量子测量破坏性本质的挑战，这种本质与不可克隆定理共同限制了从每个训练样本中可提取的信息量。本文聚焦于混合量子学习技术——将经典机器学习方法与量子算法相结合，并证明在某些设置下，由少量测量次数引起的不确定性可能成为误差的主要来源。我们通过聚焦于最大纠缠态与可分态的判别问题来识别这一可能普遍存在的现象，表明这一示例性问题对于不了解纠缠理论的学习器而言具有挑战性。最后，我们提出一种基于经典阴影的估计器，该估计器在大数据、少副本场景中表现更优。我们的结果表明，将经典机器学习方法简单应用于量子场景存在问题，因此需要建立更完善的量子学习理论基础。