correcting tilings

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

@@ -9,10 +9,15 @@ logical: qubits
 
 name: '3D color code'
 introduced: '\cite{arxiv:cond-mat/0607736}'
+# https://commons.wikimedia.org/wiki/Category:Uniform_tilings_of_Euclidean_3-space
 
 description: |
-  Three-dimensional version of the color code.
+  Color code defined on a four-valent four-colorable tiling of 3D space.
   Logical dimension is determined by the genus of the underlying surface (for closed surfaces) and types of boundaries (for open surfaces).
+  
+  There are 101 different types of boundaries for any uniform tiling \cite{arxiv:2404.05033}; this was shown for the great rhombated cubic honeycomb (a.k.a. cantitruncated cubic honeycomb) uniform tiling, but is valid for general uniform tilings.
+# Wikipedia for bitructated cubic honeycomb
+
 
 features:
   transversal_gates:

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

@@ -11,10 +11,7 @@ name: 'Cubic honeycomb color code'
 introduced: '\cite{arxiv:cond-mat/0607736}'
 
 description: |
-  3D color code defined on a four-colorable bitruncated cubic honeycomb lattice.
-
-  There are 101 different types of boundaries for a related lattice that interpolates between the bitruncated cubic honeycomb and cubic honeycomb lattices \cite{arxiv:2404.05033}.
-# Wikipedia for bitructated cubic honeycomb
+  3D color code defined on a four-colorable bitruncated cubic honeycomb uniform tiling.
 
 
 relations:

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

@@ -10,10 +10,13 @@ logical: qubits
 name: 'Tetrahedral color code'
 introduced: '\cite{arxiv:1311.0879,arxiv:1410.0069}'
 
+# https://www.youtube.com/watch?v=kTQ1p1OkLmo
+# tetrahedral-octahedral honeycomb uniform tiling
+# Tetrahedra do not tile space
 description: |
-  3D color code defined on a lattice of tetrahedra that are carved out of a BCC lattice.
+  3D color code defined on select tetrahedra of a 3D tiling.
   Qubits are placed on the vertices, edges, triangles, and in the center of each tetrahedron.
-  The code has both string-like and sheet-like logical operators \cite{arxiv:1708.07131}
+  The code has both string-like and sheet-like logical operators \cite{arxiv:1708.07131}.
 
 
 features:

codes/quantum/qubits/subsystem/topological/color/subsystem_color.yml

@@ -14,6 +14,7 @@ introduced: '\cite{arxiv:0908.4246,arxiv:1311.0879}'
 alternative_names:
   - 'Gauge color code'
 
+# https://www.wikiwand.com/en/Truncated_rhombic_dodecahedron
 description: |
   A subsystem version of the color code.
   One way to obtain it is by expanding the vertices of a two-colex embedded in a surface of genus \(g\).
@@ -44,7 +45,7 @@ relations:
   cousins:
     - code_id: color
     - code_id: single_shot
-      detail: 'The 3D subsystem color code is a single-shot code \cite{arxiv:1404.5504,arxiv:1503.08217}.'
+      detail: 'The subsystem color code defined on the cube-truncated rhombic dodecahedral honeycomb, i.e., a tesselation of cubes and chamfered cubes (a.k.a. tetratruncated rhombic dodecahedra) \cite[Fig. 1]{arxiv:1503.08217}, is a single-shot code \cite{arxiv:1404.5504,arxiv:1503.08217}.'
     - code_id: symmetry_protected_self_correct
       detail: 'A particular gauge-fixed version of a subsystem code on a 3D lattice yields a self-correcting memory protected by one-form symmetries \cite[Sec. IV D]{arxiv:1805.01474}.
       The symmetric energy barrier grows linearly with the length of a side of the lattice. When the system is coupled locally to a thermal bath respecting the symmetry and below a critical temperature, the memory time grows exponentially with the side length.