CSS code whose properties are determined from an underlying chain complex, which often consists of some type of product of other chain complexes.
- 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.
- Generalized homological-product qubit CSS code
- 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
- Homological number-phase code — Homological number-phase codes are mappings of homological rotor codes into harmonic oscillators, so they are based on the rotor version of the qubit CSS-to-homology correspondence.
- Homological bosonic code — Homological CV codes utilize chain complexes in code construction, but the complexes have trivial homology.
Page edit log
- Victor V. Albert (2022-12-04) — most recent
“Generalized homological-product CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/generalized_homological_product_css