Quantum machine learning models have shown successful generalization
performance even when trained with few data. In this work, through systematic
randomization experiments, we show that traditional approaches to understanding
generalization fail to explain the behavior of such quantum models. Our
experiments reveal that state-of-the-art quantum neural networks accurately fit
random states and random labeling of training data. This ability to memorize
random data defies current notions of small generalization error,
problematizing approaches that build on complexity measures such as the VC
dimension, the Rademacher complexity, and all their uniform relatives. We
complement our empirical results with a theoretical construction showing that
quantum neural networks can fit arbitrary labels to quantum states, hinting at
their memorization ability. Our results do not preclude the possibility of good
generalization with few training data but rather rule out any possible
guarantees based only on the properties of the model family. These findings
expose a fundamental challenge in the conventional understanding of
generalization in quantum machine learning and highlight the need for a
paradigm shift in the design of quantum models for machine learning tasks.

通过系统随机实验，我们展示了目前理解广义学习的传统方法无法解释量子模型的行为，并揭示出量子神经网络具有记忆随机数据的能力。同时，我们展示了量子神经网络可以适应任意标签的量子状态，并且这些结果阐明了量子机器学习中广义学习理解的基本挑战。