Quantum generative adversarial networks with provable convergence

Generative adversarial networks (GAN) are an important architecture in unsupervised machine learning, enabling the generation of new data produced by a desirable physical model by learning purely from an existing dataset without accessing the physical model itself. Since quantum states are the most general form of any physical data, realizing a GAN architecture in the quantum domain promises an even wider application of GANs in scientific discovery. In this work, we prove that the iterative training of a discriminator circuit against a generator circuit of previously proposed quantum GANs does not converge for certain initializations, but instead exhibits periodic oscillation between two configurations. We propose a new type of architecture for quantum generative adversarial networks (Q-GAN) to overcome such limitations by harnessing the entangling power of a quantum circuit and allowing the discriminator circuit to take both generator output and true quantum data as input. By adversarially learning efficient representations of quantum states, we prepare an approximate quantum random access memory (QRAM) and demonstrate its use in applications including the training of quantum neural networks.