Generalized homological-product CSS code 

Description

CSS code whose properties are determined from an underlying chain complex, which often consists of some type of product of other chain complexes.

Parents

Children

  • Homological rotor code — Homological rotor codes are formulated using an extension of the qubit CSS-to-homology correspondence to rotors. The homology group of the logical operators has a torsion component because the chain complexes are defined over the ring of integers, which yields codes with finite logical dimension. Products of chain complexes can also yield rotor codes.
  • Quantum check-product code
  • Quantum Tanner code
  • High-dimensional expander (HDX) code — Ramanujan codes result from a tensor product of a classical-code and a quantum-code chain complex.
  • Generalized surface code — 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.
  • Balanced product (BP) code — Balanced product codes result from a tensor product of two classical-code chain complexes, followed by a factoring out of certain symmetries.
  • Distance-balanced code

Cousin

  • Homological bosonic code — Homological CV codes utilize chain complexes in code construction, but the complexes have trivial homology.
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Zoo Code ID: generalized_homological_product_css

Cite as:
“Generalized homological-product CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/generalized_homological_product_css
BibTeX:
@incollection{eczoo_generalized_homological_product_css,
  title={Generalized homological-product CSS code},
  booktitle={The Error Correction Zoo},
  year={2022},
  editor={Albert, Victor V. and Faist, Philippe},
  url={https://errorcorrectionzoo.org/c/generalized_homological_product_css}
}
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Permanent link:
https://errorcorrectionzoo.org/c/generalized_homological_product_css

Cite as:

“Generalized homological-product CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/generalized_homological_product_css

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/properties/stabilizer/qldpc/generalized_homological_product_css.yml.