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Generalized homological-product qubit CSS code

Description

A qubit CSS code whose properties are determined from an underlying chain complex via the qubit CSS-to-homology correspondence. This complex often consists of some type of product of other chain complexes.

Cousin

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 Hamiltonian-based QECC Quantum
Parents
Qubit CSS code
Generalized homological-product CSS codeGeneralized homological-product QLDPC CSS Stabilizer Hamiltonian-based QECC Quantum
Generalized homological-product qubit CSS code
Children
Quantum rainbow codeQuantum RM code Color
Quantum pin codes are defined for simplicial complexes that admit certain colorings [2].
Fiber-bundle code
Lossless expander balanced-product code
Bicycle code
Dinur-Hsieh-Lin-Vidick (DHLV) code
Lift-connected surface (LCS) codeKitaev surface
Bivariate bicycle (BB) code
Higher-dimensional homological product code
Quantum check-product code
Dinur-Lin-Vidick (DLV) code
Generalized quantum Tanner code
Homological codeKitaev surface
The generalized surface code is constructed from chain complexes arising from cell complexes of the underlying manifold. Such complexes are not necessarily products of two non-trivial complexes, but the manifolds are picked so that their homology ensures favorable code properties.

References

[1]
C. Vuillot and N. P. Breuckmann, “Quantum Pin Codes”, IEEE Transactions on Information Theory 68, 5955 (2022) arXiv:1906.11394 DOI
[2]
T. R. Scruby, A. Pesah, and M. Webster, “Quantum Rainbow Codes”, (2024) arXiv:2408.13130
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Zoo Code ID: qubit_generalized_homological_product_css

Cite as:
“Generalized homological-product qubit CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/qubit_generalized_homological_product_css
BibTeX:
@incollection{eczoo_qubit_generalized_homological_product_css, title={Generalized homological-product qubit CSS code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/qubit_generalized_homological_product_css} }
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Permanent link:
https://errorcorrectionzoo.org/c/qubit_generalized_homological_product_css

Cite as:

“Generalized homological-product qubit CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/qubit_generalized_homological_product_css

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/qldpc/qubit_generalized_homological_product_css.yml.