transversal gates

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

@@ -36,8 +36,10 @@ protection: |
   where \(H\) is the parity-check matrix of the classical code.
 
 features:
+  transversal_gates: |
+    The three-block transversal gate mapping each \(X \to XYZ\) and each \(Z \to ZXY\) implements a logical gate \cite{arxiv:quant-ph/9702029}\cite[Exam. 2]{arxiv:quant-ph/9703048}.
+
   fault_tolerance:
-    - '\(M_3\) gate \cite{arxiv:quant-ph/9702029} can be applied to any Hermitian code \cite[Exam. 2]{arxiv:quant-ph/9703048}.'
     - 'Characterizing fault-tolerant multi-qubit gates under the \hyperref[topic:gf4-representation]{\(GF(4)\) representation} may involve characterizing all global automorphisms of some number of copies of a code that preserve the symplectic inner product \cite[pg. 9]{arxiv:quant-ph/9703048}.'
 
 

codes/quantum/qubits/stabilizer/qubit_stabilizer.yml

@@ -68,6 +68,7 @@ features:
 
   transversal_gates: 'All stabilizer codes realize Pauli transformations transversally; for a single logical qubit, these a realize dicyclic subgroup of \(SU(2)\).
   Several algorithms exist for finding logical Pauli operators \cite{arxiv:quant-ph/9705052,arxiv:0903.5256,arxiv:1803.06987}.
+  The four-block transversal gate mapping each \(X \to IXXX\) and each \(Z \to IZZZ\) implements the same logical gate on all qubits \cite{arxiv:quant-ph/9705052}.
   More generally, transversal logical gates are in a finite level of the \term{Clifford hierarchy}, which is shown using stabilizer \textit{disjointness} \cite{arxiv:1710.07256} (see also \cite{arxiv:0706.1382,arxiv:1409.8320}).
   Transversal gates for \(n\in\{1,2\}\) are semi-Clifford \cite{arxiv:0712.2084}.
   No stabilizer code can implement a classical universal gate set transversally \cite{arxiv:1704.07798}.'