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Contracting Arbitrary Tensor Networks: General Approximate Algorithm and Applications in Graphical Models and Quantum

Feng Pan1,2, Pengfei Zhou1,2, Sujie Li1,2

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We developed a general tensor network contraction method for complex inference and learning problems on graphs. This approach significantly outperforms existing methods in estimating spin glass free energy and simulating large quantum circuits.

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Area of Science:

  • Computational Physics
  • Machine Learning
  • Quantum Computing

Background:

  • Tensor networks are powerful tools for complex systems.
  • Existing contraction methods struggle with arbitrary graph connectivities.
  • Applications in inference, learning, and quantum simulations are limited by computational challenges.

Purpose of the Study:

  • To introduce a general and efficient method for approximately contracting tensor networks.
  • To enable the application of tensor network methods to a wider range of problems on general graphs.
  • To demonstrate the method's superiority over existing algorithms.

Main Methods:

  • Developed a general algorithm for approximate tensor network contraction.
  • Applied the method to graphical models, specifically spin glass free energy estimation.
  • Utilized the method for simulating random quantum circuits.

Main Results:

  • The method significantly outperforms mean-field and neural-network-based approaches for spin glass free energy estimation on various graphs.
  • Successfully simulated large quantum circuits beyond the reach of current state-of-the-art methods.
  • Achieved these results with negligible truncation errors.

Conclusions:

  • The presented tensor network contraction method offers a versatile and powerful tool for computational science.
  • It unlocks new possibilities for tackling complex inference, learning, and quantum simulation problems.
  • This work advances the practical applicability of tensor network techniques.