Learning quantum data with the quantum Earth Mover's distance
This work is significant for researchers developing quantum machine learning algorithms, as it offers a more stable and efficient method for quantifying distances in quantum data, overcoming limitations of existing metrics.
This paper addresses the issue of unstable and inefficient learning in quantum settings caused by undesirable loss landscapes of common distance metrics. It proposes using the quantum Earth Mover's (EM) distance, demonstrating its unique properties for stable and efficient quantum learning, and introduces a quantum Wasserstein generative adversarial network (qWGAN) that can learn diverse quantum data with polynomial resources.
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.