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\([[12,2,2]]\) CSS code[1]

Description

CSS code that admits a logical \(CS\) gate via application of physical \(T\) and \(T^{\dagger}\) gates.

Transversal Gates

Logical \(CS\) gate via application of physical \(T\) and \(T^{\dagger}\) gates [1].

Cousin

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Primary Hierarchy

Quantum Domain
Qubit Kingdom
Qubit codeQECC Quantum
Union stabilizer (USt) codeQECC Quantum
Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum
Coherent-parity-check (CPC) code
Qubit CSS codeCSS Stabilizer Qubit Hamiltonian-based QECC Quantum
Parents
Qubit CSS code
Small-distance qubit stabilizer codeStabilizer Hamiltonian-based Qubit Small-distance block quantum QECC Quantum
\([[12,2,2]]\) CSS code

References

[1]
M. A. Webster, A. O. Quintavalle, and S. D. Bartlett, “Transversal diagonal logical operators for stabiliser codes”, New Journal of Physics 25, 103018 (2023) arXiv:2303.15615 DOI
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Zoo Code ID: stab_12_2_2

Cite as:
“\([[12,2,2]]\) CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/stab_12_2_2
BibTeX:
@incollection{eczoo_stab_12_2_2, title={\([[12,2,2]]\) CSS code}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/stab_12_2_2} }
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Permanent link:
https://errorcorrectionzoo.org/c/stab_12_2_2

Cite as:

“\([[12,2,2]]\) CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/stab_12_2_2

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/small/stab_12_2_2.yml.