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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry.

Hao Song1,2,3, Janik Schönmeier-Kromer4,5, Ke Liu4,5

  • 1CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.

Physical Review Letters
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Summary
This summary is machine-generated.

Fracton codes offer a novel approach to quantum error correction, demonstrating significantly higher error thresholds than traditional topological codes. This makes fracton phases promising for robust quantum memory development.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Quantum Computing

Background:

  • Fracton models represent novel gapped quantum phases beyond conventional topological order.
  • These phases feature immobile excitations, offering unique properties for quantum technologies.

Purpose of the Study:

  • To calculate optimal error thresholds for quantum error correcting codes based on fracton models.
  • To investigate the potential of fracton phases as quantum memory platforms.

Main Methods:

  • Mapping error correction for bit-flip and phase-flip noise to statistical models with Ising variables and random multibody couplings.
  • Utilizing large-scale parallel tempering Monte Carlo simulations to generate disorder-temperature phase diagrams.
  • Analyzing subsystem symmetries distinct from global symmetries.

Main Results:

  • The X-cube fracton code exhibits a minimum error threshold of 7.5%, substantially higher than 3D topological codes like the toric code (3.3%) and color code (1.9%).
  • Absence of glass order at the Nishimori line was predicted.
  • The study identified unconventional subsystem symmetries in the error-correction models.

Conclusions:

  • Fracton codes demonstrate superior error resilience compared to existing 3D topological codes.
  • The findings highlight the significant potential of fracton phases for building stable and efficient quantum memory systems.