Quantum Wasserstein Generative Adversarial Networks

TL;DR

This paper introduces quantum Wasserstein GANs, a novel quantum generative model that enhances robustness and scalability on noisy quantum hardware, demonstrated through simulations and a practical circuit generation example.

Contribution

It presents the first design of quantum Wasserstein GANs, defining a quantum Wasserstein semimetric and implementing a scalable, robust quantum generative model.

Findings

Quantum WGANs outperform other quantum GANs in robustness and scalability.

Numerical simulations confirm improved performance on noisy quantum hardware.

Successfully generated a 3-qubit circuit approximating a complex Hamiltonian simulation.

Abstract

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.