  Generative adversarial networks (GANs) are a machine learning framework
comprising a generative model for sampling from a target distribution and a
discriminative model for evaluating the proximity of a sample to the target
distribution. GANs exhibit strong performance in imaging or anomaly detection.
However, they suffer from training instabilities, and sampling efficiency may
be limited by the classical sampling procedure. We introduce variational
quantum-classical Wasserstein GANs to address these issues and embed this model
in a classical machine learning framework for anomaly detection. Classical
Wasserstein GANs improve training stability by using a cost function better
suited for gradient descent. Our model replaces the generator of Wasserstein
GANs with a hybrid quantum-classical neural net and leaves the classical
discriminative model unchanged. This way, high-dimensional classical data only
enters the classical model and need not be prepared in a quantum circuit. We
demonstrate the effectiveness of this method on a credit card fraud dataset.
For this dataset our method shows performance on par with classical methods in
terms of the $F_1$ score. We analyze the influence of the circuit ansatz, layer
width and depth, neural net architecture parameter initialization strategy, and
sampling noise on convergence and performance.
