mlsanityData to 7 Oct 2026

Learning quantum data with the quantum Earth Mover's distance

arXiv 2101.03037 ↗First posted 8 Jan 2021quant-ph cs.AI cs.LGcited by 13

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Abstract (arXiv)

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.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 52 of its 152 references that are in the map. First posted on arXiv 8 Jan 2021.

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52 of 152 references.

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Citing papers per year: 2021: 1; 2022: 3; 2023: 5; 2024: 2; 2025: 1; 2026: 1.

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  1. 2024Barren Plateaus in Variational Quantum Computingcited by 130
  2. 2023Generative quantum machine learning via denoising diffusion probabilistic modelscited by 30
  3. 2022Hybrid Quantum-Classical Generative Adversarial Network for High Resolution Image Generationcited by 22
  4. 2023Explaining Quantum Circuits with Shapley Values: Towards Explainable Quantum Machine Learningcited by 17
  5. 2021Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Seriescited by 10
  6. 2023Quantum Generative Adversarial Networks: Bridging Classical and Quantum Realmscited by 6
  7. 2024Trained quantum neural networks are Gaussian processescited by 5
  8. 2022Quantum Capsule Networkscited by 3
  9. 2023Energy-dependent barren plateau in bosonic variational quantum circuitscited by 1
  10. 2026Scaling Quantum Machine Learning without Tricks: Full-Resolution and Diverse Image Generationcited by 1
  11. 2022Hybrid Quantum Generative Adversarial Networks for Molecular Simulation and Drug Discoverycited by 0
  12. 2023Quantum Wasserstein GANs for State Preparation at Unseen Points of a Phase Diagramcited by 0
1 more
  1. 2025Mean-field limit from general mixtures of experts to quantum neural networkscited by 0