Error Threshold for Color Codes and Random 3-Body Ising Models

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.

4 pages, 3 figures, 1 table

References in corpus (3)

• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Locations of multicritical points for spin glasses on regular lattices
• Error counting in a quantum error-correcting code and the ground-state energy of a spin glass

Cited by in corpus (1)

• Finite temperature topological order in 2D topological color codes