Majorana box qubit

Majorana box qubit[1–3]

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.

Gates

Braiding and fusion of MZMs, which act as Ising anyons [5,6].

Decoding

Qubit readout can be done by charge sensing [2,3,6,7].

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

Primary Hierarchy

Quantum Domain

Qubit Kingdom

Qubit codeQECC Quantum

Fermion code

Majorana stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum

Parents

Majorana stabilizer code

Small-distance qubit stabilizer codeStabilizer Hamiltonian-based Qubit Small-distance block quantum QECC Quantum

Abelian topological codeTopological Hamiltonian-based QECC Quantum

When treated as ground states of the code Hamiltonian, codewords of a single Kitaev chain realize \(\mathbb{Z}_2\) fermionic topological order.

Majorana surface codeStabilizer 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 codeStabilizer 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

Kitaev chain code

Majorana box qubit codewords span a fixed-parity subspace of the codespace of two Kitaev-chain code blocks.

Tetron code

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.