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.

翻译：量子机器学习模型即使在使用少量数据训练时，也展现出了成功的泛化性能。在本工作中，通过系统性随机化实验，我们表明传统的泛化理解方法无法解释此类量子模型的行为。我们的实验揭示，最先进的量子神经网络能够准确拟合随机态和训练数据的随机标签。这种记忆随机数据的能力违背了当前关于小泛化误差的概念，对基于VC维、Rademacher复杂度及其所有均匀相关变量等复杂性度量的方法提出了质疑。我们通过理论构造补充了实证结果，证明量子神经网络可以将任意标签拟合到量子态，暗示了其记忆能力。我们的结果并不排除使用少量训练数据实现良好泛化的可能性，而是排除了仅基于模型族属性的任何可能保证。这些发现揭示了传统泛化理解在量子机器学习中面临的根本性挑战，并强调了设计用于机器学习任务的量子模型需要范式转变。