~

codes/quantum/qubits/small_distance/small/stab_4_2_2.yml

@@ -74,9 +74,11 @@ relations:
     - code_id: surface
       detail: '\([[4,2,2]]\) code is the smallest toric code.
       Concatenating the \([[4,2,2]]\) code with the surface code is equivalent to removing stabilizer generators from the 4.8.8 color code \cite{arxiv:1604.04062}.'
-    - code_id: triangular_color
-      detail: 'The \([[4,2,2]]\) code can be interpreted as a small rectangular color code on a trapezoidal patch of four qubits that makes up two-thirds of a hexagon \cite{arxiv:2212.00042,arxiv:2305.13581}.
-      A small triangular color code is a \([[4,1,2]]\) subcode with three weight-three stabilizer generators \cite[Fig. 7]{arxiv:1806.02820}.'
+    - code_id: 2d_color
+      detail: 'The \([[4,2,2]]\) code can be interpreted as a 2D color code on a square of the 4.8.8 or 4.6.12 tilings, or on a trapezoidal patch that makes up two-thirds of a hexagon of the 6.6.6 tiling \cite{arxiv:2212.00042,arxiv:2305.13581}.
+      Concatenating the \([[4,2,2]]\) code with the surface code is equivalent to removing stabilizer generators from the 4.8.8 color code \cite{arxiv:1604.04062}.
+      Concatenating the \([[4,2,2]]\) code with two copies of the surface code yields the 4.6.12 color code \cite{arxiv:1604.04062}.
+      A small 6.6.6 color code is a \([[4,1,2]]\) subcode with three weight-three stabilizer generators \cite[Fig. 7]{arxiv:1806.02820}.'
     - code_id: hypercube_quantum
       detail: 'The \([[4,2,2]]\) code is a hypercube code for \(D=2\).'
     - code_id: iceberg
@@ -93,7 +95,7 @@ relations:
     - code_id: quantum_parity
       detail: 'The \([[4,1,2]]\) subcode \(\{|\overline{00}\rangle,|\overline{01}\rangle\}\) is the smallest member of the sub-family of \([[m^2,1,m]]\) QPC codes.'
     - code_id: stab_5_1_3
-      detail: 'The \([[4,2,2]]\) code can be derived from the five-qubit code using a protocol that converts an \([[n,k,d]]\) code into an \([[n-1, k+1, d-1]]\) code; see Sec. 3.5 in Gottesman \cite{arXiv:quant-ph/9705052}.'
+      detail: 'The \([[4,2,2]]\) code can be derived from the five-qubit code using a protocol that converts an \([[n,k,d]]\) code into an \([[n-1, k+1, d-1]]\) code \cite[Sec. 3.5]{arXiv:quant-ph/9705052}.'
     - code_id: approximate_qecc
       detail: 'The \([[4,1,2]]\) subcodes \(\{|\overline{00}\rangle,|\overline{10}\rangle\}\) \cite{arXiv:quant-ph/9704002} and \(\{|\overline{01}\rangle,|\overline{11}\rangle\}\) \cite{arxiv:quant-ph/0103042} approximately correct a single amplitude damping error, with the latter being a constant excitation code.'
     - code_id: constant_excitation
@@ -108,10 +110,6 @@ relations:
       detail: 'The \([[4,2,2]]\) code can be thought of as a concatenation of a two-qubit bit-flip with a two-qubit phase-flip code.'
     - code_id: dual_rail
       detail: 'An \(((8,1))\) constant-excitation code correcting a single amplitude damping error can be obtained from concatenating the \(\{|\overline{01}\rangle,|\overline{11}\rangle\}\) \cite{arxiv:quant-ph/0103042} subcode with the dual-rail code \cite{arxiv:2010.00538}.'
-    - code_id: 488_color
-      detail: 'Concatenating the \([[4,2,2]]\) code with the surface code is equivalent to removing stabilizer generators from the 4.8.8 color code \cite{arxiv:1604.04062}.'
-    - code_id: 4612_color
-      detail: 'The \([[4,2,2]]\) code can be concatenated with two copies of the surface code to yield the 4.6.12 color code \cite{arxiv:1604.04062}.'
     - code_id: quantum_concatenated
       detail: |
         The \([[4,2,2]]\) code can be thought of as a concatenation of a two-qubit bit-flip with a two-qubit phase-flip code.

codes/quantum/qubits/stabilizer/topological/color/2d_color/2d_color.yml

@@ -69,7 +69,7 @@ relations:
     - code_id: galois_topological
       detail: 'Galois-qudit 2D color codes reduce to 2D color codes for \(q=2\).'
     - code_id: quantum_double_abelian
-      detail: 'When treated as ground states of the code Hamiltonian, states of the color code on a torus geometry on realize \(\mathbb{Z}_2\times\mathbb{Z}_2\) topological order \cite{arxiv:0906.4127}, equivalent to the phase realized by two copies of the surface code \cite{arxiv:1503.02065}.'
+      detail: 'When treated as ground states of the code Hamiltonian, states of the color code on a torus geometry realize \(\mathbb{Z}_2\times\mathbb{Z}_2\) topological order \cite{arxiv:0906.4127}, equivalent to the phase realized by two copies of the surface code \cite{arxiv:1503.02065}.'
   cousins:
     - code_id: surface
       detail: 'The 2D color code is equivalent to multiple decoupled copies of the 2D surface code \cite{arxiv:1007.4601,arxiv:1503.02065,arXiv:1804.00866}.

codes/quantum/properties/stabilizer/topological_stabilizer/3d_stabilizer.yml → codes/quantum/qudits/stabilizer/3d_stabilizer.yml

@@ -4,7 +4,9 @@
 #######################################################
 
 code_id: 3d_stabilizer
-# includes both Galois and modular
+physical: qudits
+logical: qudits
+# there are no Galois 3D stabilizers
 
 name: '3D lattice stabilizer code'
 
@@ -18,6 +20,7 @@ description: |
 
 relations:
   parents:
+    - code_id: qudit_stabilizer
     - code_id: translationally_invariant_stabilizer
 
 

codes/quantum/properties/stabilizer/topological_stabilizer/fracton.yml → codes/quantum/qudits/stabilizer/fracton/fracton.yml

@@ -4,13 +4,15 @@
 #######################################################
 
 code_id: fracton
-# includes Galois and modular
+physical: qudits
+logical: qudits
+# there are no Galois fractons
 
 name: 'Fracton stabilizer code'
 introduced: '\cite{arXiv:1101.1962}'
 
 description: |
-  A 3D translationally invariant stabilizer code whose codewords make up the ground-state space of a Hamiltonian in a fracton phase.
+  A 3D translationally invariant modular-qudit stabilizer code whose codewords make up the ground-state space of a Hamiltonian in a fracton phase.
   Unlike topological phases, whose excitations can move in any direction, fracton phases are characterized by excitations whose movement is restricted.
 
   Fracton codes include the following three sub-types:

codes/quantum/qudits/stabilizer/fracton/qudit_cubic.yml

@@ -19,7 +19,6 @@ protection: |
 
 relations:
   parents:
-    - code_id: qudit_stabilizer
     - code_id: fracton
       detail: 'Haah cubic \cite{arXiv:1101.1962} codes 1-4, 7, 8, and 10 do not have string logical operators and are the first examples of Type-II fracton phases. The remaining cubic codes are fractal Type-I fracton codes \cite{arxiv:1908.08049,arxiv:2001.01722}.
       There is evidence that a qutrit and a \(q=5\) qudit cubic code from Ref. \cite{arXiv:1202.0052} have no string operators and are thus Type-II fracton codes (see \cite[Eqs. (D11-D13)]{arxiv:1908.08049}).'