A family of stabilizer codes for $D({\mathbb{Z}}_2)$ anyons and Majorana modes

Abstract

We study and generalize the class of qubit topological stabilizer codes that arise in the Abelian phase of the honeycomb lattice model. The resulting family of codes, which we call `matching codes' realize the same anyon model as the surface codes, and so may be similarly used in proposals for quantum computation. We show that these codes are particularly well suited to engineering twist defects that behave as Majorana modes. A proof of principle system that demonstrates the braiding properties of the Majoranas is discussed that requires only three qubits.

Published version

References in corpus (6)

• Topological Quantum Distillation
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Measurement-Only Topological Quantum Computation
• Genons, twist defects, and projective non-Abelian braiding statistics
• Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model
• Non-abelian statistics from an abelian model

Cited by in corpus (9)

• Anyon condensation and the color code
• Boundaries for the Honeycomb Code
• Tailoring quantum error correction to spin qubits
• The XYZ${}^2$ hexagonal stabilizer code
• Measurement-only topological quantum computation without forced measurements
• Data-driven decoding of quantum error correcting codes using graph neural networks
• Fermionic approach to variational quantum simulation of Kitaev spin models
• Hexagonal matching codes with 2-body measurements
• Exact results on finite size corrections for surface codes tailored to biased noise