color ref

codes/quantum/qubits/stabilizer/topological/color/3d_color/3d_color.yml

@@ -21,6 +21,8 @@ description: |
 
 features:
   transversal_gates:
+    - 'Transversal action of \(T\) gates on color codes on general 3-manifolds realizes a \(CCZ\) gate on three logical qubits and is related to a topological invariant that is called the triple intersection number \cite{arxiv:2310.16982}.'
+    - 'Transversal \(S\) gate on color codes on general 3-manifolds corresponds to a higher-form symmetry \cite{arxiv:2310.16982}.'
     - 'Universal transversal gates can be achieved using lattice surgery or code deformation \cite{arxiv:1006.5260,arxiv:0806.4827}.'
 
   general_gates:
@@ -50,6 +52,8 @@ relations:
       This mapping can also be done via code concatenation \cite{arxiv:1801.04255}.'
     - code_id: xs_stabilizer
       detail: 'The 3D color code on a particular lattice admits XS stabilizers; see \href{https://www.youtube.com/watch?v=B8h5-ANc_-8}{talk by M. Kesselring at the 2020 FTQC conference}.'
+    - code_id: spt
+      detail: 'Transversal action of \(T\) gates on color codes on general 3-manifolds realizes a \(CCZ\) gate on three logical qubits and is related to a topological invariant that is called the triple intersection number \cite{arxiv:2310.16982}. Transversal \(S\) gate on color codes on general 3-manifolds corresponds to a higher-form symmetry \cite{arxiv:2310.16982}.'
 
 
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