  The study of quantum generative models is well-motivated, not only because of
its importance in quantum machine learning and quantum chemistry but also
because of the perspective of its implementation on near-term quantum machines.
Inspired by previous studies on the adversarial training of classical and
quantum generative models, we propose the first design of quantum Wasserstein
Generative Adversarial Networks (WGANs), which has been shown to improve the
robustness and the scalability of the adversarial training of quantum
generative models even on noisy quantum hardware. Specifically, we propose a
definition of the Wasserstein semimetric between quantum data, which inherits a
few key theoretical merits of its classical counterpart. We also demonstrate
how to turn the quantum Wasserstein semimetric into a concrete design of
quantum WGANs that can be efficiently implemented on quantum machines. Our
numerical study, via classical simulation of quantum systems, shows the more
robust and scalable numerical performance of our quantum WGANs over other
quantum GAN proposals. As a surprising application, our quantum WGAN has been
used to generate a 3-qubit quantum circuit of ~50 gates that well approximates
a 3-qubit 1-d Hamiltonian simulation circuit that requires over 10k gates using
standard techniques.
