RM Majorana code

RM Majorana code[1,2]

Description

A Majorana stabilizer code constructed from a self-orthogonal RM code. These codes have the additional property that the global fermion parity is fixed in the codespace. Logical measurements are reduced to parity measurements of some subset of Majorana fermions in the code.

Protection

Code parameters are \([[2^m,2^m - \sum_{j=0}^{r} {m \choose j},2^r]]_{f}\), which are optimal per Majorana LP bounds for \(r=2\) and \(m=3,4\) [3; Sec. 3.4].

Cousin

Reed-Muller (RM) code— RM Majorana codes are constructed from self-orthogonal RM codes.

Member of code lists

Primary Hierarchy

Quantum Domain

Qubit Kingdom

Qubit codeQECC Quantum

Fermion code

Majorana stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum

Parents

Majorana stabilizer code

RM Majorana code

Children

\([[2^{m-1},2^{m-1}-m-1,4]]_{f}\) Hamming Majorana code

A Hamming Majorana code is constructed from a first-order RM code (whose dual is the extended Hamming code).

References

[1]: S. Vijay and L. Fu, “Quantum Error Correction for Complex and Majorana Fermion Qubits”, (2017) arXiv:1703.00459
[2]: G. Zeng, Y. Li, Y. Guo, and M. H. Lee, “Stabilizer quantum codes over the Clifford algebra”, Journal of Physics A: Mathematical and Theoretical 41, 145304 (2008) DOI
[3]: R. Okada, “A Quantum Analog of Delsarte’s Linear Programming Bounds”, (2025) arXiv:2502.14165

Page edit log

Victor V. Albert (2025-10-27) — most recent
Rui Okada (2025-10-27)

Cite as:

“RM Majorana code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/majorana_reed_muller

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/majorana/rm/majorana_reed_muller.yml.