Decoherence on abelian topological order is modeled as a temporal defect in double TQFT driving boundary anyon condensation transitions classified by Lagrangian subgroups of the doubled order.
Error Threshold for Color Codes and Random 3-Body Ising Models
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abstract
We study the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates suitable for entanglement distillation, teleportation and fault-tolerant quantum computation. We map the error-correction process onto a statistical mechanical random 3-body Ising model and study its phase diagram via Monte Carlo simulations. The obtained error threshold of p_c = 0.109(2) is very close to that of Kitaev's toric code, showing that enhanced computational capabilities does not necessarily imply lower resistance to noise.
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Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions
Decoherence on abelian topological order is modeled as a temporal defect in double TQFT driving boundary anyon condensation transitions classified by Lagrangian subgroups of the doubled order.