facet gate name

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

@@ -42,7 +42,7 @@ features:
     - 'Fault-tolerant logical one and logical minus state preparation in all-to-all and 2D grid connectivity \cite{arxiv:2402.17761}.'
 
   transversal_gates:
-    - 'Pauli gates are transversal, along with a non-Pauli Hadamard-phase gate \(SH\) and three-qubit Clifford operation \(M_3\) \cite{arxiv:quant-ph/9702029,arxiv:quant-ph/9705052}. These realize the \(2T\) binary tetrahedral subgroup of \(SU(2)\).'
+    - 'Pauli gates are transversal, along with a non-Pauli Hadamard-phase "facet" gate \(SH\) and three-qubit Clifford operation \(M_3\) \cite{arxiv:quant-ph/9702029,arxiv:quant-ph/9705052}. These realize the \(2T\) binary tetrahedral subgroup of \(SU(2)\).'
     - 'The code does not admit any non-Clifford transversal gates \cite{arxiv:quant-ph/9704043}; in particular, see \cite{arxiv:2011.00197} for the case of collective \(Z\) rotations.'
     - 'All transversal gates can be interpreted as monodromies under a particular notion of parallel transport \cite[Exam. 6.4.2]{arxiv:1309.7062}.'
 

codes/quantum/qubits/stabilizer/hermitian/stabilizer_over_gf4.yml

@@ -38,7 +38,7 @@ protection: |
 
 features:
   transversal_gates:
-    - 'Transversal \(SH\) and \(HS\) gates \cite[Sec. 8.2]{arxiv:quant-ph/9705052}.'
+    - 'Transversal \(SH\) and \(HS\) "facet" gates which cyclically permute Paulis as \(X \to Y\), \(Y \to Z\), and \(Z \to X\) \cite[Sec. 8.2]{arxiv:quant-ph/9705052}.'
     - 'The three-block transversal gate mapping each physical \(X \to XYZ\) and each \(Z \to ZXY\) implements a logical gate \cite{arxiv:quant-ph/9702029}\cite[Exam. 2]{arxiv:quant-ph/9703048}.'
 
   fault_tolerance:

codes/quantum/qubits/stabilizer/magic/qubit_golay.yml

@@ -33,7 +33,7 @@ features:
     - '\hyperref[topic:clifford]{Single-qubit Clifford group} by choosing \(\overline{U}=U^{\otimes 23}\) for every Clifford unitary \(U\) \cite{arxiv:1106.2190}.'
 
   general_gates:
-    - 'The Golay code can be used to perform magic-state distillation for the magic state defined as \(|T\rangle\langle T|=\frac{1}{2}(I+\frac{1}{\sqrt{3}}(X+Y+Z))\), where \(|T\rangle\) is an eigenstate of the Clifford operator \(SH\) \cite{arxiv:quant-ph/0411036}.'
+    - 'The Golay code can be used to perform magic-state distillation for the magic state defined as \(|T\rangle\langle T|=\frac{1}{2}(I+\frac{1}{\sqrt{3}}(X+Y+Z))\), where \(|T\rangle\) is an eigenstate of the Clifford "facet" gate \(SH\) \cite{arxiv:quant-ph/0411036}.'
 
   fault_tolerance:
     - 'Fault-tolerant depth-7 circuit consisting of 57 CNOT gates and preparing a logical-zero state \cite{arxiv:1106.2190}.'