Description
A Majorana stabilizer code which forms a fixed-parity subspace of the ground-state subspace of one or more Kitaev Majorana chain Hamiltonians. The \([[n,1,2]]_{f}\) Majorana box qubit forms the even-fermion-parity ground-state subspace of two parallel Kitaev Majorana chains in their fermionic topological phase. Its \([[2,1,2]]_{f}\) version is called the tetron Majorana code. An \([[3,2,2]]_{f}\) extension using three Kitaev chains and housing two logical qubits of the same parity is called the hexon Majorana code. Similarly, octon, decon, and dodecon are codes defined by the positive-parity subspace of \(4\), \(5\), and \(6\) fermionic modes, respectively [4].Protection
Errors affecting a sufficiently low but even number of Majoranas can be detected and corrected.Fault Tolerance
Fault-tolerant computation scheme [8].Cousin
- Hamiltonian-based code— A Majorana box qubit form a fixed-parity subspace of the ground-state subspace of one or more Kitaev Majorana chain Hamiltonians.
Member of code lists
- 1D stabilizer codes
- 2D stabilizer codes
- Concatenated quantum codes and friends
- Fermionic codes
- Hamiltonian-based codes and friends
- Quantum codes
- Quantum codes with fault-tolerant gadgets
- Quantum codes with notable decoders
- Quantum LDPC codes
- Qubit QLDPC codes
- Small-distance quantum codes and friends
- Stabilizer codes
- Topological codes
Primary Hierarchy
Parents
Small-distance qubit stabilizer codeStabilizer Hamiltonian-based Qubit Small-distance block quantum QECC Quantum
When treated as ground states of the code Hamiltonian, codewords of a single Kitaev chain realize \(\mathbb{Z}_2\) fermionic topological order.
The Majorana box qubit is a 1D qubit stabilizer code with respect to the Majorana operator basis.
The Majorana box qubit is a 1D qubit stabilizer code with respect to the Majorana operator basis.
Majorana surface codeQLDPC Lattice stabilizer Stabilizer Hamiltonian-based Fermion Qubit QECC Quantum
Concatenations of surface codes with Majorana box qubits are examples of Majorana surface codes [4; Table I].
Majorana color codeQLDPC Lattice stabilizer Stabilizer Hamiltonian-based Fermion Qubit Concatenated quantum QECC Quantum
Concatenations of color codes with Majorana box qubits are examples of Majorana color codes [4; Table I].
Majorana box qubit
Children
Majorana box qubit codewords span a fixed-parity subspace of the codespace of two Kitaev-chain code blocks.
The Majorana box qubit for \(n=2\) is the tetron code.
References
- [1]
- A. Y. Kitaev, “Unpaired Majorana fermions in quantum wires”, Physics-Uspekhi 44, 131 (2001) arXiv:cond-mat/0010440 DOI
- [2]
- S. Plugge, A. Rasmussen, R. Egger, and K. Flensberg, “Majorana box qubits”, New Journal of Physics 19, 012001 (2017) arXiv:1609.01697 DOI
- [3]
- T. Karzig et al., “Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes”, Physical Review B 95, (2017) arXiv:1610.05289 DOI
- [4]
- D. Litinski and F. von Oppen, “Quantum computing with Majorana fermion codes”, Physical Review B 97, (2018) arXiv:1801.08143 DOI
- [5]
- J. Alicea, Y. Oreg, G. Refael, F. von Oppen, and M. P. A. Fisher, “Non-Abelian statistics and topological quantum information processing in 1D wire networks”, Nature Physics 7, 412 (2011) arXiv:1006.4395 DOI
- [6]
- D. Aasen et al., “Milestones Toward Majorana-Based Quantum Computing”, Physical Review X 6, (2016) arXiv:1511.05153 DOI
- [7]
- J. F. Steiner and F. von Oppen, “Readout of Majorana qubits”, Physical Review Research 2, (2020) arXiv:2004.02124 DOI
- [8]
- D. Aasen et al., “Roadmap to fault tolerant quantum computation using topological qubit arrays”, (2025) arXiv:2502.12252
Page edit log
- Victor V. Albert (2023-03-07) — most recent
Cite as:
“Majorana box qubit”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/mbq
Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/majorana/mbq/mbq.yml.