Gauge color codes in two dimensions

TL;DR

This paper introduces a new family of 2D quantum error-correcting codes that enable universal quantum computation with only local operations, overcoming previous no-go theorems by using a subsystem approach and gauge fixing.

Contribution

It presents a novel 2D subsystem color code framework that supports universal gates via local measurements, bypassing topological constraints.

Findings

Supports universal gates with local operations

Circumvents no-go theorems through subsystem construction

Potential for low logical error rates despite no threshold

Abstract

We present a family of quantum error-correcting codes that support a universal set of transversal logic gates using only local operations on a two-dimensional array of physical qubits. The construction is a subsystem version of color codes where gauge fixing through local measurements dynamically determines which gates are transversal. Although the operations are local, the underlying code is not topological in structure, which is how the construction circumvents no-go constraints imposed by the Bravyi-K\"onig and Pastawski-Yoshida theorems. We provide strong evidence that the encoding has no error threshold in the conventional sense, though it is still possible to have logical gates with error probability much lower than that of physical gates.