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Universality Classes of Stabilizer Code Hamiltonians.

Zack Weinstein1, Gerardo Ortiz2, Zohar Nussinov1

  • 1Department of Physics, Washington University, St. Louis, Missouri 63130, USA.

Physical Review Letters
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Summary
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Stabilizer code quantum Hamiltonians offer robust quantum memory. Duality techniques reveal their thermodynamics, showing the 4D toric code is in the 4D Ising universality class, while Haah

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Stabilizer code quantum Hamiltonians are crucial for developing decoherence-resilient quantum memories.
  • Understanding their finite temperature thermodynamics is essential for practical quantum memory applications.

Purpose of the Study:

  • To develop a general method for solving the partition function of stabilizer code quantum Hamiltonians at finite temperatures.
  • To analyze the universality class and effective dimension of these Hamiltonians to understand their thermal properties and robustness.

Main Methods:

  • Application of duality techniques to generically solve the partition function of stabilizer codes.
  • Analysis of the 4D toric code and Haah's code as specific examples.

Main Results:

  • The 4D toric code is shown to belong to the 4D Ising universality class.
  • Haah's code demonstrates dimensional reduction, falling into the 1D Ising universality class.

Conclusions:

  • Duality techniques provide a powerful tool for analyzing the finite temperature thermodynamics of quantum memory Hamiltonians.
  • The findings offer insights into the robustness and thermal dynamics of specific quantum error-correcting codes.