diff --git a/codes/quantum/groups/rotors/stabilizer/css/homological_rotor.yml b/codes/quantum/groups/rotors/stabilizer/css/homological_rotor.yml index 6d6741685..03169a605 100644 --- a/codes/quantum/groups/rotors/stabilizer/css/homological_rotor.yml +++ b/codes/quantum/groups/rotors/stabilizer/css/homological_rotor.yml @@ -78,7 +78,7 @@ relations: parents: - code_id: rotor_stabilizer - code_id: generalized_homological_product_css - detail: 'Homological rotor codes are formulated using an extension of the \hyperref[topic:CSS-to-homology-correspondence]{qubit CSS-to-homology correspondence} to rotors. + detail: 'Homological rotor codes are constructed from chain complexes over the integers in an extension of the \hyperref[topic:CSS-to-homology-correspondence]{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.' # cousins: diff --git a/codes/quantum/oscillators/uncategorized/homological_number-phase.yml b/codes/quantum/oscillators/uncategorized/homological_number-phase.yml index f08a4eaa1..00f6d3888 100644 --- a/codes/quantum/oscillators/uncategorized/homological_number-phase.yml +++ b/codes/quantum/oscillators/uncategorized/homological_number-phase.yml @@ -40,6 +40,10 @@ relations: detail: 'Rotor analogues of \(k\)-into-\(n\) oscillator-into-oscillator GKP codes can be constructed by initializing \(n-k\) physical rotors in superpositions of phase states and applying a Clifford semigroup encoding circuit \cite{arxiv:2311.07679}.' - code_id: number_phase detail: 'Homological number-phase codes and number-phase codes are both manifestations of certain rotor codes, namely, the homological rotor codes and rotor GKP codes, respectively.' + - code_id: generalized_homological_product_css + detail: 'Homological number-phase codes are constructed from chain complexes over the integers. + 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.' # - code_id: generalized_homological_product_css # detail: 'Homological number-phase codes are mappings of \hyperref[code:homological_rotor]{homological rotor codes} into harmonic oscillators, so they are based on the rotor version of the \hyperref[topic:CSS-to-homology-correspondence]{qubit CSS-to-homology correspondence}.'