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Related Experiment Video

Updated: Jul 4, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

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Published on: August 2, 2019

Completeness of the classical 2D Ising model and universal quantum computation.

M Van den Nest1, W Dür, H J Briegel

  • 1Institut für Quantenoptik und Quanteninformation der Osterreichischen Akademie der Wissenschaften, Innsbruck, Austria.

Physical Review Letters
|June 4, 2008
PubMed
Summary

The 2D Ising model is proven to be complete, capable of representing any classical spin model. This breakthrough connects classical spin models with quantum computation, enabling new theoretical frameworks.

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Last Updated: Jul 4, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Area of Science:

  • Statistical Mechanics
  • Quantum Information Theory
  • Computational Complexity

Background:

  • Classical spin models, such as the Ising and Potts models, are fundamental in statistical mechanics for describing phase transitions and critical phenomena.
  • Understanding the computational capabilities and limitations of these models is crucial for advancing physics and computer science.
  • The concept of model completeness relates to the ability of one model to simulate another.

Purpose of the Study:

  • To establish the completeness of the 2D Ising model for representing arbitrary classical q-state spin models.
  • To provide a constructive method for mapping Ising and Potts-type models to the 2D Ising model.
  • To explore the connection between classical spin models and measurement-based quantum computation.

Main Methods:

  • Expressing the partition function of general classical q-state spin models as a special instance of the 2D Ising model partition function.
  • Developing a constructive mapping for Ising and Potts-type models to the 2D Ising model on a square lattice.
  • Leveraging the universality of 2D cluster states in measurement-based quantum computation.

Main Results:

  • The 2D Ising model is demonstrated to be computationally complete for any classical q-state spin model.
  • For Ising or Potts-type models, the mapping to the 2D Ising model requires only a polynomial increase in the number of spins.
  • For more general models, the required system size for the 2D Ising model may grow exponentially.

Conclusions:

  • The 2D Ising model serves as a universal framework for classical statistical mechanics models.
  • The established connection to measurement-based quantum computation provides new insights into the computational power of classical spin systems.
  • This work opens avenues for exploring complex spin models through the lens of quantum computation and vice versa.