  The intrinsic probabilistic nature of quantum mechanics invokes endeavors of
designing quantum generative learning models (QGLMs). Despite the empirical
achievements, the foundations and the potential advantages of QGLMs remain
largely obscure. To narrow this knowledge gap, here we explore the
generalization property of QGLMs, the capability to extend the model from
learned to unknown data. We consider two prototypical QGLMs, quantum circuit
Born machines and quantum generative adversarial networks, and explicitly give
their generalization bounds. The result identifies superiorities of QGLMs over
classical methods when quantum devices can directly access the target
distribution and quantum kernels are employed. We further employ these
generalization bounds to exhibit potential advantages in quantum state
preparation and Hamiltonian learning. Numerical results of QGLMs in loading
Gaussian distribution and estimating ground states of parameterized
Hamiltonians accord with the theoretical analysis. Our work opens the avenue
for quantitatively understanding the power of quantum generative learning
models.
