stellated color

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

@@ -69,7 +69,8 @@ relations:
     - code_id: surface
       detail: '\([[4,2,2]]\) code is the smallest toric code.'
     - code_id: triangular_color
-      detail: '\([[4,2,2]]\) 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}.'
+      detail: '\([[4,2,2]]\) 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}.'
     - code_id: ball_color
       detail: 'The \([[4,2,2]]\) code is a hyperoctahedron code for \(D=2\).'
     - code_id: iceberg
@@ -91,9 +92,7 @@ relations:
     - code_id: binomial
       detail: '\([[4,1,2]]\) subcode consisting of \(\{|\overline{00}\rangle\) and any other codeword reduces to the \(0,2,4\) binomial code when the basis labels in each codeword are written as in base-ten. Such a mapping can be generalized \cite{manual:{Linshu Li, private communication, 2018}}.'
     - code_id: heavy_hex
-      detail: 'Magic states prepared using the \([[4,1,2]]\) subcode can be injected into a largest heavy-hex code \cite{arxiv:2110.04285,arxiv:2305.13581}.'
-    - code_id: quantum_concatenated
-      detail: 'Concatenating \([[4,2,2]]\) code with surface code can generate 2D topological code with a reasonable circuit-based threshold \cite{doi:10.26421/QIC16.15-16-1}.'
+      detail: 'Magic states prepared using the \([[4,1,2]]\) subcode can be injected into the heavy-hex code \cite{arxiv:2110.04285,arxiv:2305.13581}.'
 
 
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codes/quantum/qubits/stabilizer/topological/color/2dcolor/2d_color.yml

@@ -65,7 +65,8 @@ relations:
   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}.
-      Conversely, the 2D color code can \hyperref[topic:code-switching]{condense} to form the 2D surface code in nine different ways, i.e., by adding two body hopping terms along one of its three hexagonal directions to the stabilizer group and then taking the center of the resulting nonabelian group \cite{arxiv:2212.00042}.'
+      Conversely, the 2D color code can \hyperref[topic:code-switching]{condense} to form the 2D surface code in nine different ways, i.e., by adding two body hopping terms along one of its three hexagonal directions to the stabilizer group and then taking the center of the resulting nonabelian group \cite{arxiv:2212.00042}.
+      Concatenating the \([[4,2,2]]\) code with the surface code is equivalent to removing stabilizer generators from the 4.8.8 color code \cite{doi:10.26421/QIC16.15-16-1}.'
     - code_id: 3d_color
       detail: 'Gauge fixing can be used to switch between 2D and 3D color codes, thereby yielding fault-tolerant with constant time overhead using only local quantum operations \cite{arxiv:1412.5079}.'
 

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

@@ -13,6 +13,7 @@ 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.
 
 features:
   transversal_gates: 'Universal transversal gates can be achieved using lattice surgery \cite{arXiv:1407.5103} or code deformation \cite{arxiv:1006.5260,arXiv:0806.4827}.'
@@ -33,6 +34,10 @@ relations:
   cousins:
     - code_id: 3d_surface
       detail: 'The 3D color code is equivalent to multiple decoupled copies of the 3D surface code \cite{arxiv:1007.4601,arxiv:1503.02065,arXiv:1804.00866}.'
+    - code_id: xs_stabilizer
+      detail: 'The 3D color code admits XS stabilizers; see \href{https://www.youtube.com/watch?v=B8h5-ANc_-8}{talk by M. Kesselring at the 2020 FTQC conference}.'
+    - code_id: three_fermion
+      detail: 'The 3D color code is equivalent to two decoupled copies of the 3F code \cite[Appx. B]{arxiv:1806.02820}.'
 
 
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codes/quantum/qubits/stabilizer/topological/color/stellated_color.yml

@@ -0,0 +1,33 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: stellated_color
+physical: qubits
+logical: qubits
+
+name: 'Stellated color code'
+introduced: '\cite{arxiv:1806.02820}'
+
+description: |
+  A color code on a lattice patch with a single twist defect at the center of the patch.
+
+features:
+  rate: 'Stellated color codes have negative curvature around the central defect, and thus circumvent the \hyperref[topic:BPT-bound]{BPT bound} for codes on Euclidean lattices.'
+
+relations:
+  parents:
+    - code_id: color
+  cousins:
+    - code_id: twist_defect_surface
+      detail: 'Stellated color codes are color-code analogues of twist-defect surface codes in that both encode logical information in lattice defects.
+      Instances of the former can be obtained by fattening \cite{arxiv:cond-mat/0607736} the vertices of the latter \cite{arxiv:1806.02820}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-03-10'

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

@@ -9,7 +9,7 @@ logical: qubits
 
 name: 'Twist-defect surface code'
 introduced: |
-  \cite{arxiv:1004.1838,arxiv:1612.04795,arxiv:2101.09349}
+  \cite{arxiv:1004.1838,arxiv:1612.04795,arxiv:1806.02820,arxiv:2101.09349}
 
 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.
@@ -24,6 +24,8 @@ protection: |
   Code properties depends on the number and size of the twist defects.
 
 features:
+  rate: 'Twist-defect surface codes have negative curvature around their defects, and thus circumvent the \hyperref[topic:BPT-bound]{BPT bound} for codes on Euclidean lattices.'
+
   general_gates:
     - |
       Clifford gates can be implemented via twist-based lattice surgery \cite{arxiv:2201.05678} or braiding defects

codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface/surface.yml

@@ -142,7 +142,7 @@ features:
     - '\(0.5-2.9\%\) for various noise circuit-level noise models \cite{arxiv:0803.0272,arxiv:0811.0464} (see also Refs. \cite{arXiv:quant-ph/0207088,arXiv:1311.5003}).'
     - 'Quasistatic phase damping and readout noise: \(2.85\%\) \cite{arxiv:2401.04530}.'
     - 'The toric code has a \hyperref[topic:measurement-threshold]{measurement threshold} of one \cite{arxiv:2402.00145}.'
-
+    - 'Circuit-based threshold of \(0.41\%\) when concatenated with the \([[4,2,2]]\) code \cite{doi:10.26421/QIC16.15-16-1}.'
 
 
 realizations:

codes/quantum/qubits/subsystem/topological/compass/bacon_shor.yml

@@ -91,6 +91,8 @@ relations:
   cousins:
     - code_id: hamiltonian
       detail: 'The 2D Bacon-Shor gauge-group Hamiltonian is the compass model \cite{doi:10.1070/PU1982v025n04ABEH004537,arxiv:cond-mat/0501708,arxiv:1303.5922}.'
+    - code_id: floquet
+      detail: 'The Bacon-Shor code admits a Floquet version with a particular stabilizer measurement schedule \cite{arxiv:2403.03291}.'
 
 
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