Tricolored Lattice Gauge Theory with Randomness: Fault-Tolerance in Topological Color Codes

Abstract

We compute the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates, when both qubit and measurement errors are present. By mapping the problem onto a statistical-mechanical three-dimensional disordered Ising lattice gauge theory, we estimate via large-scale Monte Carlo simulations that color codes are stable against 4.5(2)% errors. Furthermore, by evaluating the skewness of the Wilson loop distributions, we introduce a very sensitive probe to locate first-order phase transitions in lattice gauge theories.

12 pages, 5 figures, 1 table

References in corpus (3)

• Topological Quantum Distillation
• Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
• Error Threshold for Color Codes and Random 3-Body Ising Models

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