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Area of Science:

  • Quantum information science
  • Condensed matter physics
  • High-dimensional systems

Background:

  • Topological quantum error correction is crucial for robust quantum computation.
  • Toric codes offer a framework for realizing topological protection.
  • Understanding thermal effects on quantum memory is essential for practical applications.

Purpose of the Study:

  • To investigate high-dimensional generalizations of the toric code at nonzero temperatures.
  • To determine the relationship between critical temperature (Tc) and percolation temperature (Tp).
  • To identify conditions for operating a self-correcting quantum memory in the presence of defects.

Main Methods:

  • Analysis of high-dimensional toric code generalizations.
  • Thermodynamic singularity analysis to determine Tc.
  • Percolation theory to determine Tp.
  • Mean-field treatment and Monte Carlo simulations.

Main Results:

  • A distinct separation between Tc and Tp is observed in high dimensions.
  • The temperature regime Tp < T < Tc allows for self-correcting quantum memory despite percolating defects.
  • Near Tc, significant hysteresis is observed in simulations.

Conclusions:

  • A viable operating regime for self-correcting quantum memory exists at temperatures between Tp and Tc.
  • Observed hysteresis near Tc suggests potential for a 'superheated' self-correcting phase.
  • These findings advance the understanding of topological quantum error correction in realistic thermal environments.