Quantum maximum mean discrepancy GAN

Abstract Generative adversarial network (GAN) has shown profound power in machine learning. It inspires many researchers from other fields to create powerful tools for various tasks, including quantum state preparation, quantum circuit translation, and so on. It is known as classical techniques cannot efficiently simulate the quantum system, and the existing works haven’t investigated the quantum version of maximum mean discrepancy as the metric in learning models and applied it to quantum data. In this paper, we propose a metric named quantum maximum mean discrepancy (qMMD), which can be used to measure the distance between quantum data in Hilbert space. Based on the qMMD, we then design a quantum generative adversarial model, named qMMD-GAN, under the hybrid quantum–classical methods. We also provide the construction of qMMD-GAN that can be easily implemented on a quantum device. We demonstrate the power of our qMMD-GAN by applying it to a crucial real-world application that is generating an unknown quantum state. Our numerical experiments show that qMMD-GAN has a competitive performance compared to existing results. We believe that the hybrid-based models will not only be applied to physics research but provide a new direction for improving classical data processing tasks.