Topological color codes on Union Jack lattices: A stable implementation of the whole Clifford group

TL;DR

This paper investigates the error threshold of topological color codes on Union Jack lattices, demonstrating their robustness and ability to implement the full Clifford group of quantum gates through statistical mechanical modeling and simulations.

Contribution

It introduces a novel analysis of topological color codes on Union Jack lattices, showing their comparable error stability and enhanced computational capabilities.

Findings

Error thresholds similar to triangular lattices and toric codes.

Robustness of Union Jack lattice codes for quantum computation.

Full Clifford group implementation on Union Jack lattices.

Abstract

We study the error threshold of topological color codes on Union Jack lattices that allow for the full implementation of the whole Clifford group of quantum gates. After mapping the error-correction process onto a statistical mechanical random 3-body Ising model on a Union Jack lattice, we compute its phase diagram in the temperature-disorder plane using Monte Carlo simulations. Surprisingly, topological color codes on Union Jack lattices have similar error stability than color codes on triangular lattices, as well as the Kitaev toric code. The enhanced computational capabilities of the topological color codes on Union Jack lattices with respect to triangular lattices and the toric code demonstrate the inherent robustness of this implementation.