  Generalization bounds are a critical tool to assess the training data
requirements of Quantum Machine Learning (QML). Recent work has established
guarantees for in-distribution generalization of quantum neural networks
(QNNs), where training and testing data are drawn from the same data
distribution. However, there are currently no results on out-of-distribution
generalization in QML, where we require a trained model to perform well even on
data drawn from a different distribution to the training distribution. Here, we
prove out-of-distribution generalization for the task of learning an unknown
unitary. In particular, we show that one can learn the action of a unitary on
entangled states having trained only product states. Since product states can
be prepared using only single-qubit gates, this advances the prospects of
learning quantum dynamics on near term quantum hardware, and further opens up
new methods for both the classical and quantum compilation of quantum circuits.
