Learning quantum data with the quantum earth mover’s distance
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Kiani_2022_Quantum_Sci._Technol._7_045002.pdf
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15.26 MB
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Checksum (MD5)
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Author(s)
Kiani, Bobak Toussi
De Palma, Giacomo
Marvian, Milad
Liu, Zi-Wen
Lloyd, Seth
Date Issued
July 4, 2022
Journal
Quantum Science and Technology
Publisher
IOP Publishing
Citation
Bobak Toussi Kiani et al 2022 Quantum Sci. Technol. 7 045002.
Version
Final published version
Abstract
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.
Subjects
Electrical and Electronic Engineering
Physics and Astronomy (miscellaneous)
Materials Science (miscellaneous)
Atomic and Molecular Physics, and Optics
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Research Laboratory of Electronics
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1088/2058-9565/ac79c9
