2-D color code quantum computation

TL;DR

This paper details a method for universal fault-tolerant quantum computation using a 2-D color code with only nearest neighbor interactions, employing defect manipulations for logical gates.

Contribution

It introduces a novel approach to perform all single-qubit Clifford gates transversally and implements CNOT via braiding in a 2-D color code framework.

Findings

Universal fault-tolerant quantum computation is achievable with 2-D color codes.

All single-qubit Clifford gates are transversal.

CNOT gates are implemented through braiding of defects.

Abstract

We describe in detail how to perform universal fault-tolerant quantum computation on a 2-D color code, making use of only nearest neighbor interactions. Three defects (holes) in the code are used to represent logical qubits. Triple defect logical qubits are deformed into isolated triangular sections of color code to enable transversal implementation of all single logical qubit Clifford group gates. CNOT is implemented between pairs of triple defect logical qubits via braiding.