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A Bayesian inference framework for compression and prediction of quantum states.

Yannic Rath1, Aldo Glielmo2, George H Booth1

  • 1Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom.

The Journal of Chemical Physics
|October 2, 2020
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Summary

We introduce Gaussian Process States (GPS), a machine learning method to efficiently represent complex quantum states. This approach uses Bayesian inference to learn and compress quantum states, revealing key physical correlations.

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Area of Science:

  • Quantum Many-Body Physics
  • Machine Learning in Physics
  • Computational Quantum Chemistry

Background:

  • Accurate representation of quantum many-body states is computationally challenging.
  • Machine learning offers novel approaches for compact and insightful state representations.
  • Gaussian Process States (GPS) emerge as a flexible tool for quantum state modeling.

Purpose of the Study:

  • To provide a comprehensive description of learning quantum states using Gaussian Process States (GPS).
  • To demonstrate the compression of target quantum states into accurate and compact GPS representations via Bayesian inference.
  • To extract physically relevant information and correlations from quantum states.

Main Methods:

  • Utilized regression approaches based on Bayesian inference for state compression.
  • Applied a type II maximum likelihood method with relevance vector machines to identify key configurations.
  • Developed an optimization scheme for model hyperparameters to characterize correlation features.

Main Results:

  • Successfully compressed quantum states into compact and accurate GPS representations.
  • Extracted relevant many-body configurations and physical characteristics, such as correlation importance.
  • Demonstrated a tunable trade-off between model sparsity and accuracy for Fermi-Hubbard chains.

Conclusions:

  • Gaussian Process States (GPS) offer a powerful, physically insightful method for representing quantum many-body states.
  • Bayesian learning effectively extracts relevant correlations and physical properties.
  • The method shows systematic improvement and adaptability based on interaction strength and desired accuracy.