Conditional Generative Models for Learning Stochastic Processes

A framework to learn a multi-modal distribution is proposed, denoted as the conditional quantum generative adversarial network (C-qGAN). The neural network structure is strictly within a quantum circuit and, as a consequence, is shown to represent a more efficient state preparation procedure than current methods. This methodology has the potential to speed-up algorithms, such as the Monte Carlo analysis. In particular, after demonstrating the effectiveness of the network in the learning task, the technique is applied to price Asian option derivatives, providing the foundation for further research on other path-dependent options.