Power of Quantum Generative Learning (2205.04730v2)

Abstract: 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.