Majorana-XYZ subsystem code

Quantum Physics [Submitted on 27 Mar 2026] Majorana-XYZ subsystem code Tobias Busse, Lauri Toikka We present a new type of a quantum error correction code, termed Majorana-XYZ code, where the logical quantum information scales macroscopically yet is protected by topologically non-trivial degrees of freedom. It is a [n,k,g,d] subsystem code with n=L^2 physical qubits, k= \lfloor L/2 \rfloor logical qubits, g \sim L^2 gauge qubits, and distance d = L. The physical check operations, i.e. the measurements needed to obtain the error syndrome, are 3-local and nearest-neighbour. The code detects every 1- and 2-qubit error, and every error of weight 3 and higher (constrained by the distance) that is not a product of the 3-qubit check operations, however, these products act only on the gauge qubits leaving the code space invariant. The undetected weight-3 and higher operators are confined to the gauge group and do not affect logical information. While the code does not have local stabiliser generators, the logical qubits cannot be modified locally by an undetectable error, and in this sense the Majorana-XYZ code combines notions of both topological and local gauge codes while providing a macroscopic number of topological logical qubits. Taken as a non-gauge stabiliser code we can encode k \sim L^2 - 3L logical qubits into L^2 physical qubits; however, the check operators then become weight 2L. The code is derived from an experimentally promising system of Majorana fermions on the honeycomb lattice with only nearest-neighbour interactions. Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2603.26311 [quant-ph]   (or arXiv:2603.26311v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.26311 Focus to learn more Submission history From: Lauri Toikka [view email] [v1] Fri, 27 Mar 2026 11:30:07 UTC (27 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.mes-hall cond-mat.str-el References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)