steane cousin

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

@@ -97,7 +97,7 @@ relations:
     - 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: cws
-      detail: 'The five-qubit code can be formulated alternatively as a CWS code \cite{arxiv:0708.1021,manual:{Cross, Andrew William. Fault-tolerant quantum computer architectures using hierarchies of quantum error-correcting codes. Diss. Massachusetts Institute of Technology, 2008.}}.'
+      detail: 'The five-qubit perfect code is equivalent via a single-qubit Clifford circuit to a CWS code defined from a five-cycle graph and a classical repetition code \cite{arxiv:0708.1021,manual:{Cross, Andrew William. Fault-tolerant quantum computer architectures using hierarchies of quantum error-correcting codes. Diss. Massachusetts Institute of Technology, 2008.}}\cite[Table I]{arxiv:1108.5490}.'
 # - code_id: quantum_cyclic
 #   detail: 'The five-qubit code is the smallest known example of quantum cyclic code.'
 

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

@@ -96,6 +96,8 @@ relations:
   cousins:
     - code_id: quantum_cyclic
       detail: 'The Steane code is equivalent to a cyclic code via qubit permutations \cite[Exam. 1]{arxiv:1108.5490}.'
+    - code_id: cws
+      detail: 'The Steane code is equivalent via a single-qubit Clifford unitary to a CWS code defined using a particular graph and classical code \cite[Exam. 4]{arxiv:1108.5490}.'
 
 
 #      detail: 'Steane code is the smallest member of a family of Reed-Muller-based CSS codes.'