diff --git a/codes/quantum/groups/rotors/stabilizer/css/homological_rotor.yml b/codes/quantum/groups/rotors/stabilizer/css/homological_rotor.yml index 0cd59d1f2..913da88a5 100644 --- a/codes/quantum/groups/rotors/stabilizer/css/homological_rotor.yml +++ b/codes/quantum/groups/rotors/stabilizer/css/homological_rotor.yml @@ -77,8 +77,9 @@ notes: relations: parents: - code_id: rotor_stabilizer + detail: 'Homological rotor codes are rotor CSS codes 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.' - code_id: generalized_homological_product_css - detail: 'Homological rotor codes are rotor stabilizer codes 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. + detail: 'Homological rotor codes are rotor CSS codes 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/stabilizer/homological_cv.yml b/codes/quantum/oscillators/stabilizer/homological_cv.yml new file mode 100644 index 000000000..ea122f18a --- /dev/null +++ b/codes/quantum/oscillators/stabilizer/homological_cv.yml @@ -0,0 +1,34 @@ +####################################################### +## This is a code entry in the error correction zoo. ## +## https://github.com/errorcorrectionzoo ## +####################################################### + +code_id: homological_cv +physical: oscillators +logical: oscillators + +name: 'Integer-homology bosonic CSS code' +introduced: '\cite{arxiv:2411.04993}' + +description: | + An oscillator stabilizer code whose physical modes have been restricted, via a single GKP stabilizer, from the space of function on the real line to the space of periodic functions. + This restriction effectively realizes a rotor on each physical mode, allowing one to construct homological rotor codes out of displacement stabilizer groups. + 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. + + +relations: + parents: + - code_id: oscillator_stabilizer + detail: 'Integer-homology bosonic CSS codes are constructed from chain complexes over the integers and realize homological rotor codes out of displacement stabilizer groups.' + - code_id: generalized_homological_product_css + detail: 'Integer-homology bosonic CSS codes are constructed from chain complexes over the integers and realize homological rotor codes out of displacement stabilizer groups. 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.' + cousins: + - code_id: homological_rotor + detail: 'Integer-homology bosonic CSS codes are constructed from chain complexes over the integers and realize homological rotor codes out of displacement stabilizer groups.' + + +_meta: + # Change log - most recent first + changelog: + - user_id: VictorVAlbert + date: '2024-12-04' diff --git a/codes/quantum/oscillators/stabilizer/hyperplane/homological_cv.yml b/codes/quantum/oscillators/stabilizer/hyperplane/hnss.yml similarity index 99% rename from codes/quantum/oscillators/stabilizer/hyperplane/homological_cv.yml rename to codes/quantum/oscillators/stabilizer/hyperplane/hnss.yml index b050bca02..37d37e066 100644 --- a/codes/quantum/oscillators/stabilizer/hyperplane/homological_cv.yml +++ b/codes/quantum/oscillators/stabilizer/hyperplane/hnss.yml @@ -3,7 +3,7 @@ ## https://github.com/errorcorrectionzoo ## ####################################################### -code_id: homological_cv +code_id: hnss physical: oscillators logical: oscillators diff --git a/codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml b/codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml index 331174e2d..ef680ea2f 100644 --- a/codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml +++ b/codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml @@ -118,7 +118,7 @@ relations: - code_id: dual_rail detail: 'The KLM protocol can be combined with cluster states in various ways to yield MBQC protocols \cite{arxiv:quant-ph/0303008,arxiv:quant-ph/0402005,arxiv:quant-ph/0405157}.' - code_id: spt - detail: 'States realizing various SPT phases are universal resources for MBQC \cite{arxiv:1009.3491,arXiv:1009.2840,arXiv:1111.7173,arXiv:1102.5064,arXiv:1201.4877,arXiv:1301.0861,arXiv:1310.5100,arXiv:1509.02947}. A cluster-like state, or a state that is in the same SPT phase as a cluster state, can be prepared in finite time \cite{arxiv:2107.04019}.' + detail: 'States realizing various SPT phases are universal resources for MBQC \cite{arxiv:1009.3491,arXiv:1009.2840,arXiv:1111.7173,arXiv:1102.5064,arXiv:1201.4877,arXiv:1301.0861,arXiv:1310.5100,arXiv:1509.02947,arxiv:1806.08780v3}. A cluster-like state, or a state that is in the same SPT phase as a cluster state, can be prepared in finite time \cite{arxiv:2107.04019}.' - code_id: translationally_invariant_stabilizer detail: 'Cluster states can be created on various lattices \cite{arxiv:1909.11817}.'