Generalization is the ability of quantum machine learning models to make accurate predictions on new data by learning from training data. Here, we introduce the data quantum Fisher information metric (DQFIM) to determine when a model can generalize. For variational learning of unitaries, the DQFIM quantifies the amount of circuit parameters and training data needed to successfully train and generalize. We apply the DQFIM to explain when a constant number of training states and polynomial number of parameters are sufficient for generalization. Further, we can improve generalization by removing symmetries from training data. Finally, we show that out-of-distribution generalization, where training and testing data are drawn from different data distributions, can be better than using the same distribution. Our work opens up new approaches to improve generalization in quantum machine learning.

翻译：泛化是量子机器学习模型通过从训练数据中学习，对新数据做出准确预测的能力。本文引入数据量子费舍信息度量（DQFIM）来确定模型何时能够泛化。对于酉算子的变分学习，DQFIM量化了成功训练和泛化所需的电路参数与训练数据量。我们应用DQFIM解释了为何常数数量的训练态与多项式级别的参数足以实现泛化。此外，通过从训练数据中移除对称性，我们能够进一步改善泛化。最后，我们证明当训练与测试数据来自不同数据分布时，分布外泛化效果可能优于使用相同分布的情况。本研究为改进量子机器学习中的泛化性能开辟了新途径。