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Klein-bottle surface code[1]

Description

A family of Kitaev surface codes on the non-orientable Klein bottle.

Cousin

  • 3D surface code— There is a CZ gate for the 3D toric code on a Klein bottle \(\times S^1\) [2].

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
Homological code
Kitaev surface codeCDSC Twist-defect surface Lattice stabilizer Generalized homological-product QLDPC CSS Stabilizer Qubit Abelian topological Topological Hamiltonian-based QECC Quantum
Parents
Kitaev surface code
The Klein bottle surface code is the surface code on a Klein bottle.
Klein-bottle surface code

References

[1]
X. Zou and H.-K. Lo, “Algebraic Topology Principles behind Topological Quantum Error Correction”, (2025) arXiv:2505.06082
[2]
M. Barkeshli, Y.-A. Chen, P.-S. Hsin, and R. Kobayashi, “Higher-group symmetry in finite gauge theory and stabilizer codes”, SciPost Physics 16, (2024) arXiv:2211.11764 DOI
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Zoo Code ID: klein_bottle

Cite as:
“Klein-bottle surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/klein_bottle
BibTeX:
@incollection{eczoo_klein_bottle, title={Klein-bottle surface code}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/klein_bottle} }
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Permanent link:
https://errorcorrectionzoo.org/c/klein_bottle

Cite as:

“Klein-bottle surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/klein_bottle

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/klein_bottle.yml.