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Generative quantum learning of joint probability distribution functions

Sep 13, 2021
17 pages
Published in:
  • Phys.Rev.Res. 4 (2022) 4, 043092
  • Published: Nov 8, 2022
e-Print:
DOI:
Report number:
  • 995073.2.0
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Abstract: (APS)
Modeling joint probability distributions is an important task in a wide variety of fields. One popular technique for this employs a family of multivariate distributions with uniform marginals called copulas. While the theory of modeling joint distributions via copulas is well understood, it gets practically challenging to accurately model real data with many variables. In this paper, we show that any copula can be naturally mapped to a multipartite maximally entangled state. Thus, the task of learning joint probability distributions becomes the task of learning maximally entangled states. We prove that a variational ansatz we christen as a “qopula” based on this insight leads to an exponential advantage over classical methods of learning some joint distributions. As an application, we train a quantum generative adversarial network (QGAN) and a quantum circuit Born machine (QCBM) using this variational ansatz to generate samples from joint distributions of two variables in historical data from the stock market. We demonstrate our generative learning algorithms on trapped ion quantum computers from IonQ for up to eight qubits. Our experimental results show interesting findings such as the resilience against noise, outperformance against equivalent classical models and 20–1000 times less iterations required to converge as compared to equivalent classical models.
Note:
  • 19 pages, 11 figures. v2: published version
  • machine learning: quantum
  • computer: quantum
  • variational
  • network
  • ion
  • entanglement
  • qubit
  • distribution function
  • [1]
    (, New York, )
    • G. James
      ,
    • D. Witten
      ,
    • T. Hastie
      ,
    • R. Tibshirani
  • [2]

    Portfolio selection

    • H. Markowitz
  • [3]
    (, New York, )
    • S. Zacks
  • [4]
    1st edition (, New York, )
    • C.C. Aggarwal
  • [5]
    (, Cambridge, )
    • H.v. Storch
      ,
    • F.W. Zwiers
  • [6]

    Statistics of medical imaging

    • C. Palmer
  • [7]

    Global financial crisis, extreme interdependencies, and contagion effects: The role of economic structure?

    • R. Aloui
      ,
    • M.S.B. Aissa
      ,
    • D.K. Nguyen
  • [7]

    Asset markets contagion during the global financial crisis

    • D. Kenourgios
      ,
    • A. Christopoulos
      ,
    • D.I. Dimitriou
  • [7]

    Upper tail dependence in rainfall extremes: Would we know it if we saw it?

    • F. Serinaldi
      ,
    • A. Bárdossy
      ,
    • C.G. Kilsby
  • [8]
    Fonctions de repartition a n dimensions et leurs marges, Publications de l'Institut Statistique de l'Université de Paris
    • M. Sklar
  • [9]

    Bivariate option pricing using dynamic copula models

    • R.W. van den Goorbergh
      ,
    • C. Genest
      ,
    • B.J. Werker
  • [10]

    Estimating joint flow probabilities at stream confluences by using copulas

    • R.T. Kilgore
      ,
    • D.B. Thompson
  • [11]

    Segmenting multi-source images using hidden Markov fields with copula-based multivariate statistical distributions

    • J. Lapuyade-Lahorgue
      ,
    • J.-H. Xue
      ,
    • S. Ruan
  • [12]
    (, New York, )
    • H. Joe
  • [13]
    Generative adversarial nets, in Advances in Neural Information Processing Systems (NIPS 27)
    • I. Goodfellow
      ,
    • J. Pouget-Abadie
      ,
    • M. Mirza
      ,
    • B. Xu
      ,
    • D. Warde-Farley
    et al.
  • [14]
    Auto-encoding variational Bayes, in 2nd International Conference on Learning Representations, ICLR 2014, Banff, AB, Canada, April 14-16, 2014, Conference Track Proceedings, edited by
    • Y. Bengio
      ,
    • Y. LeCun
      ,
    • D.P. Kingma
      ,
    • M. Welling
    • [15]

      Data augmentation generative adversarial Networks

      • A. Antoniou
        ,
      • A. Storkey
        ,
      • H. Edwards
    • [16]
      Learning a probabilistic latent space of object shapes via 3D generative-adversarial modeling, in Advances in Neural Information Processing Systems 29: Annual Conference on Neural Information Processing Systems 2016, December 5-10, 2016, Barcelona, Spain, NIPS'16 (, USA, ), pp
      • J. Wu
        ,
      • C. Zhang
        ,
      • T. Xue
        ,
      • B. Freeman
        ,
      • J. Tenenbaum
    • [17]
      Photo-realistic single image super-resolution using a generative adversarial network, in 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (, ), pp
      • C. Ledig
        ,
      • L. Theis
        ,
      • F. Huszár
        ,
      • J. Caballero
        ,
      • A. Cunningham
      et al.
    • [18]
      Do GANs learn the distribution? Some theory and empirics, in International Conference on Learning Representations (, )
      • S. Arora
        ,
      • A. Risteski
        ,
      • Y. Zhang
    • [19]
      Common problems—Generative adversarial networks—Google Developers, https://developers.google.com/machine-learning/gan/problems
      • [20]
        The computational complexity of linear optics, in Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing, STOC '11 (, USA, ), pp
        • S. Aaronson
          ,
        • A. Arkhipov
      • 1-25 of 70
      • 1
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      • 3
      • 25 / page