Tetron Majorana code

Tetron Majorana code[1–3]

Description

Also called a Majorana box qubit or Majorana qubit. An \([[n,2,2]]_{f}\) Majorana stabilizer code forming the even-fermion-parity ground-state subspace of two parallel Kitaev Majorana chains in their fermionic topological phase. An extension using three Kitaev chains and housing two logical qubits of the same parity is called the hexon Majorana code.

Protection

Single Majorana operators are detectable because they map the even-parity codespace into an odd-parity error space.

Gates

Braiding and fusion of MZMs, which act as Ising anyons [4,5].

Decoding

Qubit readout can be done by charge sensing [2,3,5,6].

Parents

Majorana stabilizer code
Small-distance block quantum code
Abelian topological code — When treated as ground states of the code Hamiltonian, surface codewords realize, codewords of a single Kitaev chain realize \(\mathbb{Z}_2\) fermionic topological order. The MZMs used to define the tetron code act as Ising anyons, which are nonabelian.

Child

Kitaev chain code — Kitaev chain codewords can be obtained by restricting to only one Kitaev chain out of the two chains that define the tetron Majorana code.

Cousin

Hamiltonian-based code — The tetron code forms the ground-state subspace of two Kitaev Majorana chain Hamiltonians.

References

[1]: A. Y. Kitaev, “Unpaired Majorana fermions in quantum wires”, Physics-Uspekhi 44, 131 (2001) arXiv:cond-mat/0010440 DOI
[2]: S. Plugge et al., “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]: J. Alicea et al., “Non-Abelian statistics and topological quantum information processing in 1D wire networks”, Nature Physics 7, 412 (2011) arXiv:1006.4395 DOI
[5]: D. Aasen et al., “Milestones Toward Majorana-Based Quantum Computing”, Physical Review X 6, (2016) arXiv:1511.05153 DOI
[6]: J. F. Steiner and F. von Oppen, “Readout of Majorana qubits”, Physical Review Research 2, (2020) arXiv:2004.02124 DOI

Page edit log

Victor V. Albert (2023-03-07) — most recent

Cite as:

“Tetron Majorana code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/mbq

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qubits/fermions/mbq.yml.