refs

codes/quantum/qubits/stabilizer/qubit_css.yml

@@ -126,7 +126,7 @@ features:
     - 'Transversal Pauli gates since qubit CSS codes are qubit stabilizer codes.'
     - 'Transversal CNOT gates preserve the logical subspace, up to \(X\)-type Paulis, iff a qubit stabilizer code is CSS \cite{arxiv:quant-ph/9605011,preset:GottesmanBook}. The Paulis are necessary for when the code is stabilized by stabilizers with a minus in front of them, e.g., \(-XXXX\) and \(ZZZZ\).'
     - 'Self-dual CSS codes admit a transversal Hadamard gate.'
-    - '\textit{Fold-transversal} \cite{arxiv:2202.06647} Clifford gates are transversal gates combined with qubit permutations. Some of these can be obtained from automorphism groups of the underlying classical codes \cite[Thms. 2-3]{arxiv:1302.1035}.'
+    - '\textit{Fold-transversal} \cite{arxiv:1603.02286,arxiv:2202.06647} Clifford gates are transversal gates combined with qubit permutations. Some of these can be obtained from automorphism groups of the underlying classical codes \cite[Thms. 2-3]{arxiv:1302.1035}.'
     - 'Necessary and sufficient conditions for a CSS code to yield a transversal gate in the \term{Clifford hierarchy} have been formulated \cite[Thm. 9]{arxiv:2109.13481}\cite[Thm. 5]{arxiv:2204.13176}\cite{arxiv:2406.00425}.
     There are routines that can determine what diagonal gates in the \term{Clifford hierarchy} are realized by a code \cite{arxiv:2303.15615,manual:{Webster, Mark. The XP Stabilizer Formalism. Dissertation, University of Sydney, 2023.}}.'
   general_gates:

codes/quantum/qubits/stabilizer/qubit_stabilizer.yml

@@ -121,6 +121,7 @@ features:
     - '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}.'
+    - 'Fold-transversal gates have been extended from qubit CSS codes to qubit stabilizer codes, and there is an algorithm to determine them from the stabilizer group \cite{arxiv:2409.18175}.'
 
   general_gates:
     - 'Logical Clifford gates can be performed by physical Clifford circuits that permute logical Pauli operators \cite{arxiv:1803.06987}.'

codes/quantum/qudits_galois/stabilizer/qldpc/lp/scalar/2bga.yml

@@ -99,7 +99,7 @@ protection: |
 
 features:
   transversal_gates:
-    - 'Logical Pauli operators and fold-transversal gates studied in Ref. \cite{arxiv:2407.03973}.'
+    - 'Logical Pauli operators and fold-transversal gates have been studied \cite{arxiv:2407.03973,arxiv:2409.18175}.'
 
   rate: |-
     The 2BGA construction gives some of the best short codes with small stabilizer weights.