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

TL;DR

This paper estimates the error threshold of topological color codes in quantum computing, demonstrating their robustness against certain error rates through statistical-mechanical modeling and simulations.

Contribution

It introduces a novel mapping of color code error correction to a disordered Ising lattice gauge theory and estimates the error threshold using large-scale Monte Carlo simulations.

Findings

Color codes are stable against approximately 4.5% errors.

A new probe based on Wilson loop skewness detects phase transitions.

The study advances understanding of fault-tolerance in topological quantum 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.