qutrit_pauli_gkp_subcode

codes/classical/spherical/polytope/4d/600cell/600cell.yml

@@ -41,6 +41,8 @@ relations:
       detail: 'The 600-cell and 120-cell are dual to each other.'
     - code_id: 120cell
       detail: 'Vertices of a 120-cell can be split up into vertices of five 600-cells \cite{preset:coxeter,arxiv:1309.7530}. The 600-cell and 120-cell are dual to each other.'
+    - code_id: icosahedron
+      detail: 'A realization of the 600-cell in terms of quaternion coordinates yields the 120 elements of the binary icosahedral group \(2I\) \cite{arxiv:2205.04965}.'
 
 
 # Begin Entry Meta Information

codes/quantum/oscillators/stabilizer/oscillator_stabilizer.yml

@@ -7,7 +7,7 @@ code_id: oscillator_stabilizer
 physical: oscillators
 
 name: 'Bosonic stabilizer code'
-introduced: '\cite{arxiv:quant-ph/0405064,arxiv:1210.3637}'
+introduced: '\cite{arxiv:quant-ph/0405064,arxiv:1210.3637,arxiv:2411.04993}'
 
 alternative_names:
   - 'CV stabilizer code'

codes/quantum/oscillators/uncategorized/qutrit_pauli_gkp_subcode.yml

@@ -0,0 +1,33 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: qutrit_pauli_gkp_subcode
+physical: oscillators
+logical: qubits
+
+name: 'Qutrit-Pauli group-representation code'
+introduced: '\cite{arxiv:2410.18713}'
+
+description: |
+  A subcode of a two-mode GKP code whose projection is onto a copy of an irreducible representation of the \hyperref[topic:qudit-pauli]{single-qutrit Pauli group}, the symmetry group of the \(\{3,3,3\}\) tesselation of real space.
+  The code admits the corresponding gates via displacements and phase-space rotations.
+
+
+relations:
+  parents:
+    - code_id: oscillators
+    - code_id: group_representation
+      detail: 'The qutrit-Pauli group-representation code is a group-representation code with \(G\) being the \hyperref[topic:qudit-pauli]{single-qutrit Pauli group}.'
+  cousins:
+    - code_id: multimodegkp
+      detail: 'The qutrit-Pauli group-representation code is a subcode of a two-mode GKP code \cite{arxiv:2410.18713}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2023-11-28'

codes/quantum/qubits/permutation_invariant/icosahedral_permutation_invariant.yml

@@ -43,6 +43,8 @@ relations:
   cousins:
     - code_id: steane
       detail: 'The Pollatsek-Ruskai code can be continuously deformed to the Steane code \cite{arxiv:2410.07983}.'
+    - code_id: icosahedron
+      detail: 'Binary icosahedral group \(2I\) gates can be realized transversally in the Pollatsek-Ruskai code \cite{arxiv:2305.07023}.'
 
 
 # Begin Entry Meta Information

codes/quantum/spins/many_spin/t_group.yml

@@ -15,7 +15,7 @@ description: |
   Groups which admit irreps with this property are called \textit{twisted (unitary) \(1\)-groups} and include the binary icosahedral group \(2I\), the \(\Sigma(360\phi)\) subgroup of \(SU(3)\), the family \(\{PSp(2b, 3), b \geq 1\}\), and the alternating groups \(A_{5,6}\).
   Groups whose irreps are images of the appropriate irreps of twisted \(1\)-groups also yield such properties, e.g., the binary tetrahedral group \(2T\) or qutrit Pauli group \(\Sigma(72\phi)\).
 
-  A \(((3,2,2))_3\) code can implement the qutrit Pauli group \(\Sigma(72\phi)\) transversally, a \(((6,3,2))\) code can implement \(A_5\) transversally, a \(((6,2,2))_3\) implements \(2T\) transversally, and a \(((6,5,2))_3\) code implements \(A_6\) transverally.
+  A \(((3,2,2))_3\) code can implement the qutrit Pauli group \(\Sigma(72\phi)\) transversally, a \(((6,3,2))\) code can implement \(A_5\) transversally, a \(((6,2,2))_3\) implements \(2T\) transversally, and a \(((6,5,2))_3\) code implements \(A_6\) transversally.
 
 features:
   transversal_gates: