~

codes/classical/q-ary_digits/q-ary_digits_into_q-ary_digits.yml

@@ -19,7 +19,7 @@ protection: |
 
   \begin{defterm}{Weight enumerator}
   \label{topic:weight-enumerator}
-  Determining protection and bounds on code parameters can also be done using the \textit{weight enumerator} \cite{arxiv:quant-ph/9610040} (cf. \hyperref[topic:quantum-weight-enumerator]{quantum weight enumerators}),
+  Determining protection and bounds on code parameters can also be done using the code's \textit{weight enumerator} \cite{arxiv:quant-ph/9610040} (cf. \hyperref[topic:quantum-weight-enumerator]{quantum weight enumerators}),
     \begin{align}
     \begin{split}
       A(x,y)&=\sum_{j=0}^{n}A_{j}x^{n-j}y^{j}\\

codes/quantum/qubits/dynamic_gen/da/da.yml

@@ -38,7 +38,7 @@ relations:
     - code_id: dynamic_gen
       detail: 'DA code state initialization, logical gates, and error correction are done by a sequence of different (usually weight-two) stabilizer measurements.'
   cousins:
-    - code_id: 2d_color
+    - code_id: triangular_color
       detail: 'The parent topological phase of the 2D DA color code is realized by two copies of the 2D color code.'
     - code_id: 3d_color
       detail: 'The parent topological phase of the 3D DA color code is realized by three copies of the 3D color code.'

codes/quantum/qubits/nonstabilizer/cws/rains.yml

@@ -16,7 +16,7 @@ description: |
 relations:
   parents:
     - code_id: cws
-      detail: 'The \(((5+2r,3\times 2^{2r+1},2))\) qubit code family whose graph state is the union of the ring and Bell-pair graphs \cite{arxiv:quant-ph/9704043} is a CWS family \cite{arxiv:0708.1021,manual:{Cross, Andrew William. Fault-tolerant quantum computer architectures using hierarchies of quantum error-correcting codes. Diss. Massachusetts Institute of Technology, 2008.}}.'
+      detail: 'The \(((5+2r,3\times 2^{2r+1},2))\) qubit code family is a CWS family whose graph state is the union of the ring and Bell-pair graphs \cite{arxiv:0708.1021,manual:{Cross, Andrew William. Fault-tolerant quantum computer architectures using hierarchies of quantum error-correcting codes. Diss. Massachusetts Institute of Technology, 2008.}}.'
     - code_id: small_distance_quantum
 
 

codes/quantum/qubits/qubits_into_qubits.yml

@@ -41,7 +41,7 @@ protection: |
 
   \begin{defterm}{Quantum weight enumerator}
   \label{topic:quantum-weight-enumerator}
-  Determining protection and bounds on code parameters can also be done using the Shor-Laflamme \textit{quantum weight enumerator} \cite{arxiv:quant-ph/9610040} (cf. \hyperref[topic:weight-enumerator]{weight enumerators})
+  Determining protection and bounds on code parameters can also be done using the code's Shor-Laflamme \textit{quantum weight enumerator} \cite{arxiv:quant-ph/9610040} (cf. \hyperref[topic:weight-enumerator]{weight enumerators})
     \begin{align}
     \begin{split}
       A(x)&=\sum_{j=0}^{n}A_{j}x^{j}\\

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

@@ -76,9 +76,7 @@ relations:
       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 \([[4,1,2]]\) code with three weight-three stabilizer generators \cite[Fig. 7]{arxiv:1806.02820}.
-      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}.
-      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}.'
+      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: hypercube_quantum
       detail: 'The \([[4,2,2]]\) code is a hypercube code for \(D=2\).'
     - code_id: iceberg
@@ -110,6 +108,10 @@ 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/small_distance/small/stab_6_4_2.yml

@@ -39,13 +39,13 @@ relations:
     - code_id: iceberg
       detail: 'The \([[2m,2m-2,2]]\) error-detecting code for \(m=3\) reduces to the \([[6,4,2]]\) error-detecting code.'
     - code_id: triangular_color
-      detail: 'The \([[6,4,2]]\) error-detecting code can be interpreted as a color code on a single hexagon of a honeycomb lattice.
-      The \([[6,4,2]]\) code can be concatenated with the surface code to yield the honeycomb color code \cite[Appx. A]{arxiv:1604.04062}.'
+      detail: 'The \([[6,4,2]]\) error-detecting code is a color code defined on a single hexagon of the 6.6.6 tiling.
+      The \([[6,4,2]]\) code can be concatenated with the surface code to yield the 6.6.6 color code \cite[Appx. A]{arxiv:1604.04062}.'
     - code_id: small_distance_quantum
   cousins:
     - code_id: quantum_concatenated
       detail: 'Concatenations of this code with itself yield the level-\(r\) \([[6^r,4^r,2^r]]\) many-hypercube code \cite{arxiv:2403.16054}.
-      The \([[6,4,2]]\) code can be concatenated with the surface code to yield the honeycomb color code \cite[Appx. A]{arxiv:1604.04062}.'
+      The \([[6,4,2]]\) code can be concatenated with the surface code to yield the 6.6.6 color code \cite[Appx. A]{arxiv:1604.04062}.'
     - code_id: stab_4_2_2
       detail: 'The \([[6,4,2]]\) error-detecting code can be constructed out of two \([[4,2,2]]\) codes in the quantum Lego code framework.'
     - code_id: quantum_lego

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

@@ -85,7 +85,7 @@ features:
 relations:
   parents:
     - code_id: triangular_color
-      detail: 'Steane code is the smallest triangular color code.'
+      detail: 'Steane code is a 2D color code defined on a seven-qubit patch of the 6.6.6 tiling.'
     - code_id: diagonal_clifford
     - code_id: quantum_hamming_css
     - code_id: single_qubit_clifford

codes/quantum/qubits/stabilizer/fermion_into_qubit/derby_klassen.yml

@@ -26,7 +26,7 @@ relations:
   cousins:
     - code_id: xzzx
       detail: 'The DK code encodes fermions into excitations of the Wen plaquette model \cite{arxiv:2009.11860}.'
-    - code_id: triangular_color
+    - code_id: 2d_color
       detail: 'The DK code on several tilings resembles the 2D color code with some vertex qubits removed \cite{manual:{Derby, Charles. Compact fermion to qubit mappings for quantum simulation. Diss. UCL (University College London), 2023.}}.'
 
 

codes/quantum/qubits/stabilizer/magic/triorthogonal/stab_49_1_5.yml

@@ -28,8 +28,8 @@ relations:
   cousins:
     - code_id: doubled_color
       detail: 'The \([[49,1,5]]\) triorthogonal code can be viewed as a (gauge-fixed) doubled color code obtained from the \([[17,1,5]]\) 2D color code via the doubling transformation \cite{arxiv:1509.03239}.'
-    - code_id: 2d_color
-      detail: 'The \([[49,1,5]]\) triorthogonal code can be viewed as a (gauge-fixed) doubled color code obtained from the \([[17,1,5]]\) 2D color code via the doubling transformation \cite{arxiv:1509.03239}.'
+    - code_id: 488_color
+      detail: 'The \([[49,1,5]]\) triorthogonal code can be viewed as a (gauge-fixed) doubled color code obtained from the \([[17,1,5]]\) 4.8.8 color code via the doubling transformation \cite{arxiv:1509.03239}.'
 
 
 # Begin Entry Meta Information

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

@@ -16,7 +16,6 @@ alternative_names:
 description: |
   Color code defined on a two-dimensional trivalent planar graph with three-colorable faces.
   The three uniform tilings of this type are the 6.6.6 (honeycomb) tiling, the 4.8.8 (square octagon) tiling, and the 4.6.12 tiling \cite[Fig. 1]{arxiv:1108.5738}.
-  The code is called triangular because finite subsets of the uniform tilings typically take the shape of triangles.
   Each face hosts two stabilizer generators, a Pauli-\(X\) and a Pauli-\(Z\) string acting on all the qubits of the face.
 
   Logical dimension is determined by the genus of the underlying surface (for closed surfaces) and the types of boundaries (for open surfaces).
@@ -26,9 +25,9 @@ description: |
   These paths can have branching points. Each path has two string operators, one corresponding to the \(X\) basis and one corresponding to the \(Z\) basis.
   In correspondence with the coloring of the lattice faces, string operators also come in three colors.
   A string of one color must end in a boundary of that same color.
-  String operators commute or anti-commute.
-  They anti-commute when they cross an odd number of times and have a different color and type.
 
+# String operators commute or anti-commute.
+# They anti-commute when they cross an odd number of times and have a different color and type.
 # \begin{figure}
   #   \includegraphics{colorCodeHoneycombHighlightedChecksAdjColor.svg}
   #   \caption{Stabilizer generators and string operators of a 2D color code defined on a honeycomb lattice on a torus.

codes/quantum/qubits/stabilizer/topological/color/2d_color/non-css/twist_defect_color.yml

@@ -16,7 +16,7 @@ alternative_names:
 description: |
   A non-CSS extension of the 2D color code whose non-CSS stabilizer generators are associated with twist defects of the associated lattice.
 
-  For lattices with dislocations and rotational disclinations, twist-defect stabilizer generators are placed at the location of the dislocations to yield a stabilizer code whose logical dimension depends on the defects.
+  For lattices with dislocations and rotational disclinations, twist-defect stabilizer generators are placed at the location of the dislocations.
   Logical dimension is determined by the genus of the underlying surface (for closed surfaces), types of boundaries (for open surfaces), and any twist defects present.
 
 protection: |

codes/quantum/qubits/stabilizer/topological/color/2d_color/non-css/xyz_color.yml

@@ -26,9 +26,9 @@ relations:
     - code_id: 2d_stabilizer
   cousins:
     - code_id: triangular_color
-      detail: 'The XYZ surface code is obtained from the 6.6.6 color code by applying single-qubit Cliffors rotations on a subset of qubits such that the \(X\)- and \(Z\)-type generators are mapped to \(XZXZXZ\) and \(ZYZYZY\), respectively.'
+      detail: 'The XYZ color code is obtained from the 6.6.6 color code by applying single-qubit Clifford rotations on a subset of qubits such that the \(X\)- and \(Z\)-type generators are mapped to \(XZXZXZ\) and \(ZYZYZY\), respectively.'
     - code_id: xzzx
-      detail: 'The XZZX surface (XYZ color) is a non-CSS analogue of the rotated surface (6.6.6 color) code such that the two codes are related by single-qubit Cliffors rotations.'
+      detail: 'The XZZX surface (XYZ color) is a non-CSS analogue of the rotated surface (6.6.6 color) code such that the two codes are related by single-qubit Clifford rotations.'
 
 
 # Begin Entry Meta Information

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

@@ -11,8 +11,6 @@ name: 'Honeycomb (6.6.6) color code'
 short_name: '6.6.6 color'
 introduced: '\cite{arxiv:quant-ph/0605138}'
 
-
-
 description: |
   Triangular color code defined on a patch of the 6.6.6 (honeycomb) tiling.
 

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

@@ -12,7 +12,7 @@ introduced: '\cite{arxiv:cond-mat/0607736}'
 
 description: |
   Three-dimensional version of the color code.
-  Logical dimension is determined by the genus of the underlying surface (for closed surfaces), types of boundaries (for open surfaces), and/or any twist defects \cite{arxiv:1806.02820} present.
+  Logical dimension is determined by the genus of the underlying surface (for closed surfaces) and types of boundaries (for open surfaces).
 
 features:
   transversal_gates: 'Universal transversal gates can be achieved using lattice surgery or code deformation \cite{arxiv:1006.5260,arXiv:0806.4827}.'

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

@@ -12,23 +12,28 @@ introduced: '\cite{arxiv:quant-ph/0605138}'
 # not a lattice code because can be defined on general graph
 
 description: |
-  Member of a family of CSS codes defined on a \(D\)-dimensional graph which satisfies two properties: The graph is (1) a homogeneous simplicial \(D\)-complex obtained as a triangulation of the interior of a \(D\)-simplex and (2) is \(D+1\)-colorable.
+  Member of a family of CSS codes defined on a \(D\)-dimensional graph which satisfies two properties: (1) the graph is a homogeneous simplicial \(D\)-complex obtained as a triangulation of the interior of a \(D\)-simplex, and (2) the graph is \(D+1\)-colorable.
+  Qubits are placed on the \(D\)-simplices and generators are supported on suitable simplices \cite{arXiv:1311.0277,doi:10.7907/059V-MG69}.
 
-  Qubits are placed on the \(D\)-simplices and generators are supported on suitable simplices \cite{doi:10.7907/059V-MG69}.
-  For 2-dimensional color code, the lattice must be such that it is 3-valent and has 3-colorable faces, such as a honeycomb lattice.
-  The qubits are placed on the vertices and two stabilizer generators are placed on each face \cite{arXiv:1311.0277}.
+# For 2-dimensional color code, the lattice must be such that it is 3-valent and has 3-colorable faces, such as a honeycomb lattice.
+# The qubits are placed on the vertices and two stabilizer generators are placed on each face \cite{arXiv:1311.0277}.
 
 
 protection: |
   As with the surface code, the code distance depends on the specific kind of lattice used to define the code. More precisely, the distance depends on the homology of logical string operators \cite{arXiv:1311.0277}.
 
-  In contrast to the surface code, the color code can suffer from unremovable hook errors due to the specifics of its syndrome extraction circuits. Fault-tolerant decoders thus have to utilize additional flag qubits.
-
 
 features:
+  decoders:
+    - 'In contrast to the surface code, the color code can suffer from unremovable hook errors due to the specifics of its syndrome extraction circuits.
+    Fault-tolerant decoders thus have to utilize additional flag qubits.'
   fault_tolerance:
     - 'The 6D color code is a self-correcting quantum memory and admits fault-tolerant universal gate set in 7D \cite{arXiv:0907.5228}.'
 
+notes:
+  - 'See Ref. \cite{arXiv:1311.0277} for an overview of color codes.'
+
+
 relations:
   parents:
     - code_id: quantum_pin

codes/quantum/qubits/stabilizer/topological/surface/non-css/twist_defect_surface.yml

@@ -18,8 +18,9 @@ description: |
   A non-CSS extension of the 2D surface-code construction whose non-CSS stabilizer generators are associated with twist defects of the associated lattice.
 
   For lattices with dislocations and rotational disclinations, twist-defect stabilizer generators are placed at the location of the dislocations to yield a stabilizer code whose logical dimension depends on the defects.
-  A simple example is a surface code on a lattice with a single lattice dislocation which hosts a weight-five non-CSS twist-defect stabilizer generator \cite[Fig. 2]{arxiv:1004.1838}.
+  Logical dimension is determined by the genus of the underlying surface (for closed surfaces), types of boundaries (for open surfaces), and any twist defects present.
 
+  A simple example is a surface code on a lattice with a single lattice dislocation which hosts a weight-five non-CSS twist-defect stabilizer generator \cite[Fig. 2]{arxiv:1004.1838}.
   More generally, given a graph embedded in a 2D manifold, qubits are placed on vertices, stabilizers on faces, and twist defects are associated to odd-degree vertices.
 
 

codes/quantum/qubits/stabilizer/topological/surface/non-css/xysurface.yml

@@ -25,6 +25,7 @@ relations:
   parents:
     - code_id: clifford-deformed_surface
       detail: XY code is obtained from the surface code by applying \(H\sqrt{Z}H\) to all qubits, thereby exchaning \(Z\leftrightarrow Y\).
+    - code_id: quantum_double_abelian
   cousins:
     - code_id: heavy_hex
       detail: 'XY surface code can be adapted for a heavy-hexagonal lattice \cite{arxiv:2211.14038}.'

codes/quantum/qubits/stabilizer/topological/surface/non-css/xzzx/xzzx.yml

@@ -59,6 +59,7 @@ relations:
   parents:
     - code_id: clifford-deformed_surface
       detail: XZZX code is obtained from the rotated surface code by applying Hadamard gates on a subset of qubits such that \(XXXX\) and \(ZZZZ\) generators are both mapped to \(XZXZ\).
+    - code_id: quantum_double_abelian
   cousins:
     - code_id: rotated_surface
       detail: 'XZZX code is obtained from the rotated surface code by applying Hadamard gates on a subset of qubits such that \(XXXX\) and \(ZZZZ\) generators are both mapped to \(XZXZ\). Both rotated and XZZX codes offer improved performance over the original surface code for biased noise \cite{arxiv:2312.17057}.'

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

@@ -27,8 +27,8 @@ relations:
     - code_id: quantum_divisible
       detail: 'Doubled color codes are subsystem codes constructed using a generalization of the doubling transformation \cite{arxiv:1012.4134} that combines doubly-even linear binary codes to make triply-even codes.
       The doubling transformation is a special case of level lifting (from two to three) \cite[Sec. VI.D]{arxiv:1709.08658}.'
-    - code_id: 2d_color
-      detail: 'Doubled color codes can be obtained by pipelining \cite{arxiv:1703.07847} 2D color codes \cite[Sec. VI.D]{arxiv:1709.08658}.'
+    - code_id: 488_color
+      detail: 'Doubled color codes can be obtained by pipelining \cite{arxiv:1703.07847} 4.8.8 color codes \cite[Sec. VI.D]{arxiv:1709.08658}.'
 # quantum_divisible is not parent because doubled_color is subsystem
 
 

codes/quantum/qubits/subsystem/topological/subsystem_three_fermion.yml

@@ -29,7 +29,7 @@ relations:
     - code_id: three_fermion
       detail: 'The (three-dimensional) 3F Walker-Wang model cluster-like state encodes the temporal gate operations on the (two-dimensional) 3F subsystem code into a third spatial dimension \cite{arxiv:2011.04693}.'
     - code_id: 2d_color
-      detail: 'The 2D color code is equivalent to two decoupled copies of the 3F code in the sense that the same anyon theory describes the low-energy excitations of both codes \cite[Appx. B]{arxiv:1806.02820}.'
+      detail: 'The 2D color code is equivalent to two decoupled copies of the 3F code in the sense that the same anyon theory describes the low-energy excitations of both codes \cite[Appx. B]{arxiv:1806.02820}\cite{manual:{Zhenghan Wang. private communication, 2017.}}.'
 
 # In addition, one of possible 2D boundaries of the 3F Walker-Wang model code is effectively a 3F subsystem code.