\([[13,1,5]]\) twisted toric code

\([[13,1,5]]\) twisted toric code[1]

Description

Thirteen-qubit twisted toric code whose stabilizer tableau consists of cyclic permutations of the \(XZZX\)-type Pauli string \(XIZZIXIIIIIII\). The code can be thought of as a small twisted XZZX code [1; Exam. 11 and Fig. 3].

Transversal Gates

No non-Pauli transversal gates.

Member of code lists

Primary Hierarchy

Quantum Domain

Qubit Kingdom

Qubit codeQECC Quantum

Union stabilizer (USt) codeQECC Quantum

Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum

Qubit QLDPC codeStabilizer Hamiltonian-based QECC Quantum

Twist-defect surface codeLattice stabilizer Stabilizer Hamiltonian-based QECC Quantum

XZZX surface code

Twisted XZZX toric codeCyclic quantum QECC Quantum

Parents

Twisted XZZX toric code

The \([[13,1,5]]\) twisted toric code is a small twisted XZZX toric code [1; Exam. 11 and Fig. 3].

Frobenius codeStabilizer Hamiltonian-based Cyclic quantum QECC Quantum

Hermitian qubit codeStabilizer Hamiltonian-based Qubit QECC Quantum

The \([[13,1,5]]\) twisted toric code is Hermitian [2; ID 67067199e766ad364e845262].

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

\([[13,1,5]]\) twisted toric code

References

[1]: A. A. Kovalev, I. Dumer, and L. P. Pryadko, “Design of additive quantum codes via the code-word-stabilized framework”, Physical Review A 84, (2011) arXiv:1108.5490 DOI
[2]: S. Burton, “qecdb.org: Quantum Error Correction Database”, URL

Page edit log

Simon Burton (2024-07-17) — most recent
Victor V. Albert (2024-07-17)
Victor V. Albert (2024-03-31)

Cite as:

“\([[13,1,5]]\) twisted toric code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/stab_13_1_5

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/small/13/stab_13_1_5.yml.