ref - 3d surface

Author: valbert4

codes/quantum/qubits/stabilizer/qubit_css.yml

@@ -131,6 +131,7 @@ features:
     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.}}.'
     - 'CSS code families with asymptotic rate \(> 1/3\) and distance at \(\geq 3\) do not admit logical qubit permutations from physical permutations \cite{arxiv:2502.13889}.'
     - 'Self-dual CSS codes admit the group \(Sp(2\ell,\mathbb{F}_2)\) of diagonal transversal gates on \(\ell\) codeblocks \cite{arxiv:2507.10519}.'
+    - 'Diagonal transversal gate groups can be defined using a set of equations \cite{arxiv:2601.21514}.'
   general_gates:
     - 'LDPC CSS code symmetries called \(XZ\)-dualities allow for fold-transversal gates, i.e., transversal gates followed by qubit permutations \cite{arxiv:2202.06647}.'
     - 'Generalized lattice surgery \cite{arxiv:2301.13738}.'

codes/quantum/qubits/stabilizer/topological/surface/higher_d/3d_fermionic_surface.yml

@@ -41,7 +41,7 @@ relations:
       detail: 'The 3D fermionic surface code is a Walker-Wang model code with premodular input category \(\mathcal{C} = \text{sVec}\) consisting of a trivial anyon and a fermion.'
     - code_id: 3d_stabilizer
     - code_id: topological_abelian
-      detail: 'The 3D Kitaev surface code realizes 3D \(\mathbb{Z}_2\) gauge theory with fermionic charge and bosonic loop excitations (FcBl), i.e., with an emergent fermion.'
+      detail: 'The 3D fermionic surface code realizes 3D \(\mathbb{Z}_2\) gauge theory with fermionic charge and bosonic loop excitations (FcBl), i.e., with an emergent fermion. The fermionic excitations endow the code with an anomalous two-form symmetry, which is argued to induce a non-trivial finite-temperature topological order \cite{arxiv:2503.02928}.'
   cousins:
     - code_id: 3d_surface
       detail: 'The 3D (fermionic) surface code is a CSS (non-CSS) code which realizes a \(\mathbb{Z}_2\) gauge theory in 3D (with an emergent fermion). Two copies of the 3D fermionic surface code are equivalent to a copy of the 3D surface code and a copy of the 3D fermionic surface code via anyon relabeling: the two incoming fermions, \(f_1\) and \(f_2\), can be re-organized into a boson \(f_1 f_2\) and fermion \(f_2\).'