~

codes/quantum/oscillators/coherent_state/qsc.yml

@@ -55,6 +55,9 @@ relations:
     - code_id: coherent_constellation
       detail: 'Coherent-state QSCs are coherent-state constellation codes constrained to lie on a sphere.'
   cousins:
+    - code_id: group_representation
+      detail: 'QSCs should be able to be formulated as group-representation codes whose group is that formed by the permutation representation of the code polytope symmetry group.
+      It remains to show that the permutation representation is irreducible.'
     - code_id: points_into_spheres
       detail: 'QSCs are quantum analogues of spherical and constant-energy codes because they store information in quantum superpositions of points on a sphere in quantum phase space.'
     - code_id: spherical

codes/quantum/oscillators/fock_state/constant_excitation/one_hot_quantum.yml

@@ -19,7 +19,7 @@ protection: |
 features:
   general_gates:
     - 'Non-deterministic gates using linear optics and photon-number resolving detectors \cite{arxiv:2302.07357}.'
-    - 'If the code is embedded into Fock space, the group \(SU(q)\) can be realized via Gaussian rotations \cite{arxiv:2306.11621}.'
+    - 'The group \(SU(q)\) can be realized via Gaussian rotations \cite{arxiv:2306.11621}.'
 
 
 relations:
@@ -28,7 +28,7 @@ relations:
     - code_id: constant_excitation
     - code_id: permutation_invariant
     - code_id: group_representation
-      detail: 'One-hot quantum codes are group-representation codes with \(G = SU(q)\) \cite{arxiv:2306.11621}.'
+      detail: 'One-hot quantum codes are group-representation codes with the \(G = SU(q)\) subgroup of Gaussian rotations \cite{arxiv:2306.11621}.'
   cousins:
     - code_id: one_hot
       detail: 'The one-hot quantum code is the quantum version of the one-hot code.'

codes/quantum/qubits/small_distance/small/stab_5_1_3.yml

@@ -68,8 +68,8 @@ relations:
       detail: 'The \([[5,1,3]]_{\mathbb{Z}_q}\) modular-qudit code for \(q=2\) reduces to the five-qubit perfect code.'
     - code_id: galois_5_1_3
       detail: 'The \([[5,1,3]]_q\) Galois-qudit code for \(q=2\) reduces to the five-qubit perfect code.'
-    - code_id: quantum_cyclic
-      detail: 'The five-qubit code is the smallest known example of quantum cyclic code.'
+    - code_id: group_representation
+      detail: 'The five-qubit code is a group-representation code with \(G\) being the \(2T\) subgroup of \(SU(2)\) \cite{arxiv:2306.11621}.'
   cousins:
     - code_id: hamiltonian
       detail: 'The five-qubit code Hamiltonian is local when expressed in terms of mutually commuting Majorana operators \cite{manual:{Aleksander Kubica, private communication, 2019}}.'
@@ -79,8 +79,8 @@ relations:
       detail: 'Every \(((5,2,3))\) code is equivalent to the five-qubit code \cite[Corr. 10]{arxiv:quant-ph/9704043}.'
     - code_id: quantum_concatenated
       detail: 'The concatenated five-qubit code has a \hyperref[topic:measurement-threshold]{measurement threshold} of one \cite{arxiv:2402.00145}.'
-    - code_id: group_representation
-      detail: 'The five-qubit code is a group-representation code with \(G\) being the \(2T\) subgroup of \(SU(2)\) \cite{arxiv:2306.11621}.'
+# - code_id: quantum_cyclic
+#   detail: 'The five-qubit code is the smallest known example of quantum cyclic code.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/small_distance/small/steane.yml

@@ -71,12 +71,12 @@ relations:
     - code_id: diagonal_clifford
     - code_id: quantum_hamming_css
     - code_id: single_qubit_clifford
+    - code_id: group_representation
+      detail: 'The Steane code is a group-representation code with \(G\) being the \(2O\) subgroup of \(SU(2)\) \cite{arxiv:2306.11621}.'
   cousins:
     - code_id: quantum_concatenated
       detail: 'The concatenated Steane code is one of the first codes to admit a concatenated threshold \cite{arxiv:quant-ph/9702058,arxiv:quant-ph/9809054,arxiv:quant-ph/0207119}. Randomized compiling helps reduce logical error rate for some noise models \cite{arxiv:2303.06846}.
       The concatenated Steane code has a \hyperref[topic:measurement-threshold]{measurement threshold} of one \cite{arxiv:2402.00145}.'
-    - code_id: group_representation
-      detail: 'The Steane code is a group-representation code with \(G\) being the \(2O\) subgroup of \(SU(2)\) \cite{arxiv:2306.11621}.'
 
 
 #      detail: 'Steane code is the smallest member of a family of Reed-Muller-based CSS codes.'

codes/quantum/spins/single_spin/su3_spin.yml

@@ -18,7 +18,7 @@ relations:
   parents:
     - code_id: single_spin
     - code_id: group_representation
-      detail: '\(SU(3)\) spin codes are group-representation codes with \(G\) being a subgroup of \(SU(2)\) \cite{arxiv:2306.11621}.'
+      detail: '\(SU(3)\) spin codes are group-representation codes with \(G\) being a subgroup of \(SU(3)\) \cite{arxiv:2306.11621}.'
 
 
 # Begin Entry Meta Information