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.

arXiv commentPublished version

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Cited by in corpus (17)

• Poking holes and cutting corners to achieve Clifford gates with the surface code
• Anyon condensation and the color code
• The boundaries and twist defects of the color code and their applications to topological quantum computation
• Boundaries for the Honeycomb Code
• Universal fault-tolerant measurement-based quantum computation
• Demonstrating non-Abelian braiding of surface code defects in a five qubit experiment
• Benchmarking near-term devices with quantum error correction
• Tailoring quantum error correction to spin qubits
• Parafermions in a Kagome lattice of qubits for topological quantum computation
• The XYZ${}^2$ hexagonal stabilizer code
• Active error correction for Abelian and non-Abelian anyons
• 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
• Continuous error correction for Ising anyons
• Hexagonal matching codes with 2-body measurements
• Exact results on finite size corrections for surface codes tailored to biased noise