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

TL;DR

This paper investigates the error threshold of color codes in quantum computing by mapping the problem onto a 3-body Ising model and finds that their noise resistance is comparable to the toric code.

Contribution

It introduces a mapping of color code error correction onto a 3-body Ising model and determines the error threshold through Monte Carlo simulations.

Findings

Error threshold p_c ≈ 0.109(2) for color codes

Color codes have similar noise resistance to toric codes

Enhanced computational capabilities do not reduce noise tolerance

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.