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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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Machine-learning study using improved correlation configuration and application to quantum Monte Carlo simulation.

Yusuke Tomita1, Kenta Shiina2,3, Yutaka Okabe2

  • 1College of Engineering, Shibaura Institute of Technology, Saitama 330-8570, Japan.

Physical Review. E
|September 18, 2020
PubMed
Summary

This study introduces an improved correlation estimator for machine learning phase classification in spin models. It successfully classifies phases of the quantum XY model using classical model training data.

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Area of Science:

  • Statistical Mechanics
  • Machine Learning
  • Quantum Physics

Background:

  • Machine learning is increasingly used for classifying phases of matter in complex physical systems.
  • Traditional correlation estimators can have limitations in accurately capturing phase transitions.
  • Understanding quantum phase transitions, like the Berezinskii-Kosterlitz-Thouless transition, is crucial in condensed matter physics.

Purpose of the Study:

  • To introduce and evaluate a novel Fortuin-Kasteleyn representation-based improved estimator for correlation configuration.
  • To apply this improved estimator to the machine learning-based phase classification of classical and quantum spin models.
  • To analyze the Berezinskii-Kosterlitz-Thouless transition in the spin-1/2 quantum XY model and classify its phases.

Main Methods:

  • Utilizing the Fortuin-Kasteleyn representation-based improved estimator as an alternative to ordinary correlation configuration.
  • Applying machine learning algorithms for phase classification of spin models.
  • Employing the loop algorithm in quantum Monte Carlo simulations.
  • Training machine learning models on classical XY model data to classify quantum XY model phases.

Main Results:

  • The improved estimator effectively classifies phases of classical spin models.
  • The method successfully classifies the Berezinskii-Kosterlitz-Thouless and paramagnetic phases of the spin-1/2 quantum XY model.
  • Classification of the quantum XY model's phases was achieved using training data from the classical XY model.

Conclusions:

  • The Fortuin-Kasteleyn representation-based improved estimator offers a viable alternative for machine learning-based phase classification.
  • Machine learning, aided by improved estimators, can effectively analyze quantum phase transitions.
  • Cross-model training (classical to quantum) demonstrates the robustness and transferability of the machine learning approach for phase classification.