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Area of Science:

  • Condensed Matter Physics
  • Quantum Information Science
  • Statistical Mechanics

Background:

  • Decoherence of topological order (TO) is critical for open quantum matter and decoding transitions.
  • Non-Abelian TOs are key to understanding error thresholds in stabilizer codes.

Purpose of the Study:

  • To develop statistical mechanical models for decohering non-Abelian TOs.
  • To analyze the stability of non-Abelian TOs against quantum channels.
  • To inform error-correction strategies for topological quantum memories.

Main Methods:

  • Statistical mechanical modeling using loop models.
  • Analysis of Rényi-n moments as coupled O(N) loop models.
  • Diagonalization of the density matrix at maximal error rate.
  • Exact results for Kitaev quantum double models and numerical simulations for the Kitaev honeycomb model.

Main Results:

  • Decohered density matrices are described by loop models with topological loop weight N (quantum dimension).
  • Rényi-n moments map to coupled O(N) loop models.
  • Non-Abelian TOs exhibit remarkable stability against quantum channels that proliferate anyons with large quantum dimensions.
  • Critical phases emerge for smaller quantum dimensions.

Conclusions:

  • Non-Abelian topological order demonstrates robustness against specific types of quantum proliferation.
  • The findings provide a theoretical framework for understanding error resilience in topological quantum memories.
  • This work suggests potential for robust topological quantum computation using non-Abelian anyons.