A family of stabilizer codes for D(ℤ₂) anyons and Majorana modes

2015/01/31 by James R. Wootton · 24 citations
Mathematics · Physics and Astronomy · #Abelian group #Advanced Condensed Matter Physics #Anyon #Combinatorics #Discrete mathematics #Fermion #Lattice (music) #MAJORANA #Mathematics #Physics #Quantum #Quantum computer #Quantum many-body systems #Quantum mechanics #Qubit #Theoretical physics #Topological Materials and Phenomena #Topological quantum computer #Topology (electrical circuits) #Toric code #Twist #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1088/1751-8113/48/21/215302

published in Journal of Physics A Mathematical and Theoretical 48(21), 215302 (Institute of Physics) · Published version

openalex publication_date 2015/05/06 · arxiv created 2015/05/13 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Introduction to Topological Quantum Computation
• Topological quantum memory
• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Lifetime of topological quantum memories in thermal environment
• Measurement-Only Topological Quantum Computation

Cited by

• Demonstrating non-Abelian braiding of surface code defects in a five qubit experiment
• Poking Holes and Cutting Corners to Achieve Clifford Gates with the Surface Code
• Universal fault-tolerant measurement-based quantum computation