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\([[8,2,2]]\) hyperbolic color code[1]

Description

An \([[8,2,2]]\) hyperbolic color code defined on the projective plane.

Transversal Gates

Applying transversal \(S\) and \(S^{\dagger}\), \(\sqrt{X}\), and Hadamard gates yields various logical gates [2].

Cousin

  • \([[9,1,3]]\) Shor code— The Shor code (\([[8,2,2]]\) color code) is a small surface (color) code defined on the projective plane.

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
Coherent-parity-check (CPC) code
Qubit CSS codeCSS Stabilizer Qubit Hamiltonian-based QECC Quantum
Generalized homological-product qubit CSS codeGeneralized homological-product QLDPC CSS Stabilizer Hamiltonian-based QECC Quantum
Quantum rainbow code
Quantum pin codeStabilizer Hamiltonian-based Qubit QECC Quantum
Color code
Hyperbolic color code
Parents
Hyperbolic color code
The \([[8,2,2]]\) hyperbolic color code is defined on the projective plane.
Small-distance qubit stabilizer codeStabilizer Hamiltonian-based Qubit Small-distance block quantum QECC Quantum
\([[8,2,2]]\) hyperbolic color code

References

[1]
C. Vuillot and N. P. Breuckmann, “Quantum Pin Codes”, IEEE Transactions on Information Theory 68, 5955 (2022) arXiv:1906.11394 DOI
[2]
H. Chen, M. Vasmer, N. P. Breuckmann, and E. Grant, “Automated discovery of logical gates for quantum error correction (with Supplementary (153 pages))”, Quantum Information and Computation 22, 947 (2022) arXiv:1912.10063 DOI
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Zoo Code ID: stab_8_2_2

Cite as:
“\([[8,2,2]]\) hyperbolic color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/stab_8_2_2
BibTeX:
@incollection{eczoo_stab_8_2_2, title={\([[8,2,2]]\) hyperbolic color code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/stab_8_2_2} }
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Permanent link:
https://errorcorrectionzoo.org/c/stab_8_2_2

Cite as:

“\([[8,2,2]]\) hyperbolic color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/stab_8_2_2

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/small/8/stab_8_2_2.yml.