hnss (integer-homology bosonic CSS)

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:

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'

codes/quantum/oscillators/stabilizer/hyperplane/homological_cv.yml → 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
 

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}.'