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errorcorrectionzoo · Feb 21, 2024 · 602b8fc · 602b8fc
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diff --git a/codes/quantum/properties/group_representation.yml b/codes/quantum/properties/group_representation.yml
@@ -14,7 +14,7 @@ description: |
 
 features:
   encoders:
-    - 'General encoding map \cite{arxiv:2306.11621}.'
+    - 'General encoding map \cite[Lemma 1]{arxiv:2306.11621}.'
   general_gates:
     - 'By definition, a group \(G\) of gates can be realized on the code using the unitary operations used to define the code.'
 

diff --git a/codes/quantum/qubits/small_distance/small/stab_5_1_3.yml b/codes/quantum/qubits/small_distance/small/stab_5_1_3.yml
@@ -79,6 +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}.'
 
 
 # Begin Entry Meta Information

diff --git a/codes/quantum/qubits/small_distance/small/steane.yml b/codes/quantum/qubits/small_distance/small/steane.yml
@@ -75,6 +75,9 @@ relations:
     - 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 five-qubit 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.'
 #      detail: 'Steane code is the smallest member of a family of quantum Hamming codes.'

diff --git a/codes/quantum/spins/single_spin/su3_spin.yml b/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 \(SU(2)\).'
+      detail: '\(SU(3)\) spin codes are group-representation codes with \(G\) being a subgroup of \(SU(2)\) \cite{arxiv:2306.11621}.'
 
 
 # Begin Entry Meta Information