Learning quantum data with the quantum earth mover's distance

Quantifying how far the output of a learning algorithm is from its target is an essential task in machine learning. However, in quantum settings, the loss landscapes of commonly used distance metrics often produce undesirable outcomes such as poor local minima and exponentially decaying gradients. To overcome these obstacles, we consider here the recently proposed quantum earth mover's (EM) or Wasserstein-1 distance as a quantum analog to the classical EM distance. We show that the quantum EM distance possesses unique properties, not found in other commonly used quantum distance metrics, that make quantum learning more stable and efficient. We propose a quantum Wasserstein generative adversarial network (qWGAN) which takes advantage of the quantum EM distance and provides an efficient means of performing learning on quantum data. We provide examples where our qWGAN is capable of learning a diverse set of quantum data with only resources polynomial in the number of qubits.

Automated summary

This paper introduces a solution to the problem of commonly used distance metrics in machine learning in quantum settings. It proposes a quantum EM distance as a quantum analog to the classical EM distance, which possesses unique properties that make quantum learning more stable and efficient. The paper also presents a quantum Wasserstein generative adversarial network (qWGAN) that takes advantage of the quantum EM distance for learning on quantum data.