Majorana subsystem stabilizer code[1]
Description
Subsystem stabilizer code whose gauge group is generated by products of Majorana operators. Logical information is encoded in physical fermionic modes, with some encoded degrees of freedom designated as gauge qubits.
The measured checks need not commute, the stabilizer group is the center of the check group, and the logical group is its normalizer [2; Sec. II D]. Such codes can be denoted by \([[n,k,g,d]]_{f}\), where \(n\) is the number of fermionic modes, \(g\) is the number of gauge qubits, and \(d\) is the least Majorana weight of a nontrivial dressed logical operator. Codes with no gauge qubits reduce to Majorana stabilizer codes, denoted \([[n,k,d]]_{f}\).
In tetron constructions, placing tetron parity operators in the gauge group makes it possible to diagnose parity-violating errors without fixing each tetron parity using high charging energy, while requiring fewer stabilizer generators than an earlier non-subsystem construction with the same error-correction capability [1].
Cousins
- Fermion code— Majorana subsystem stabilizer codes encode logical information into a physical Fock space of fermionic modes, with some degrees of freedom designated as gauge qubits.
- Majorana stabilizer code— A Majorana subsystem stabilizer code with no gauge qubits is a Majorana stabilizer code.
- Majorana-XYZ code— In the thermodynamic limit, the (originally qubit-based) Majorana-XYZ code has a Majorana-fermion formulation as the strong-interaction limit of the honeycomb-lattice Majorana-Hubbard model [3], whose four-Majorana interaction terms play the role of the gauge generators. The two models are related by a Jordan-Wigner transformation [4; Appx. A].
Member of code lists
Primary Hierarchy
References
- [1]
- S. Kundu and B. Reichardt, “Majorana subsystem qubit codes that also correct odd-weight errors”, New Journal of Physics 26, 073029 (2024) DOI
- [2]
- A. J. Landahl and B. C. A. Morrison, “Logical fermions for fault-tolerant quantum simulation”, (2023) arXiv:2110.10280
- [3]
- C. Li and M. Franz, “Majorana-Hubbard model on the honeycomb lattice”, Physical Review B 98, (2018) arXiv:1806.06092 DOI
- [4]
- T. Busse and L. Toikka, “Majorana-XYZ subsystem code”, (2026) arXiv:2603.26311
Page edit log
- Victor V. Albert (2026-08-25) — most recent
- Victor V. Albert (2026-08-24)
- Victor V. Albert (2026-06-08)
- Victor V. Albert (2024-07-09)
Cite as:
“Majorana subsystem stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/majorana_subsystem, arXiv:2606.11484