twist defect surface

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

@@ -58,6 +58,8 @@ relations:
       Electric and magnetic operators on the embedded surface code correspond to outer logical operators of the Floquet code.
       In fact, outer logical operators transition back and forth from magnetic to electric surface code operators under the measurement dynamics.
       Inspired by this code, stabilizer measurement circuits consisting of two-body measurements have been designed for the surface code \cite{arxiv:2007.00307,arxiv:2206.12780}.'
+    - code_id: twist_defect_surface
+      detail: 'Fermionic string excitations of the honeycomb Floquet code can be condensed along one-dimensional paths, yielding twist defects \cite{arxiv:2306.08027}.'
     - code_id: subsystem_color
       detail: 'Both honeycomb and subsystem color codes are generated via periodic sequences of measurements. However, any measurement sequence can be performed on the color code without destroying the logical qubits, while honeycomb codes can be maintained only with specific sequences. Honeycomb codes require a shorter measurement cycle and use fewer qubits at the given code distance \cite{arXiv:2107.02194}.'
     - code_id: majorana_stab

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

@@ -15,7 +15,8 @@ description: |
 
 relations:
   parents:
-    - code_id: clifford-deformed_surface
+    - code_id: twist_defect_surface
+      detail: 'The rhombic dodecahedron surface code is a twist-defect surface code whose degree-three vertices can be interpreted as disclination twists \cite{arXiv:2010.06628}.'
     - code_id: small_distance_quantum
   cousins:
     - code_id: polytope

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

@@ -0,0 +1,49 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: twist_defect_surface
+physical: qubits
+logical: qubits
+
+name: 'Twist-defect surface code'
+introduced: |
+  \cite{arxiv:1004.1838,arxiv:1612.04795,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 topological phase.
+
+  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}.
+
+  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.
+
+
+protection: |
+  Code properties depends on the number and size of the twist defects.
+
+features:
+  general_gates:
+    - |
+      Clifford gates can be implemented via twist-based lattice surgery \cite{arxiv:2201.05678} or braiding defects
+      \cite{arxiv:0704.2540,arxiv:1004.1838,arXiv:1104.5047,arXiv:1208.0928,arXiv:1508.04166,arXiv:1609.04673,arXiv:2103.08381}.
+
+realizations:
+  - |
+    Ground state of the toric code has been implemented with and without twists, and the non-Abelian braiding behavior of the twists, which realize Ising anyons, has been demonstrated \cite{arxiv:2211.09802}.
+
+relations:
+  parents:
+    - code_id: qubit_stabilizer
+    - code_id: 2d_stabilizer
+  cousins:
+    - code_id: topological_abelian
+      detail: 'Twist-defect surface codes realize \(\mathbb{Z}_2\) topological order with twist defects.'
+
+
+# Begin Entry Meta Information
+_meta:
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-02-13'

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

@@ -77,9 +77,7 @@ features:
   general_gates:
     - |
       Clifford gates can be implemented via lattice surgery
-      \cite{arXiv:1111.4022,arXiv:1709.02318,arXiv:1808.02892,arXiv:2109.02746},
-      twist-based lattice surgery \cite{arxiv:2201.05678}, or braiding defects
-      \cite{arxiv:0704.2540,arxiv:1004.1838,arXiv:1104.5047,arXiv:1208.0928,arXiv:1508.04166,arXiv:1609.04673,arXiv:2103.08381}.
+      \cite{arXiv:1111.4022,arXiv:1709.02318,arXiv:1808.02892,arXiv:2109.02746}.
     - |
       Non-Clifford gates require magic state distillation
       \cite{arXiv:1905.06903}, Dehn twists \cite{arxiv:1806.06078}, or
@@ -142,6 +140,13 @@ features:
 
 
 
+
+realizations:
+  - |
+    One cycle of syndrome readout on 19-qubit planar and 24-qubit toric codes realized in two-dimensional Rydberg atomic arrays \cite{arxiv:2112.03923}.
+  - |
+    Signatures of corresponding topological phase of matter detected in superconducting circuits \cite{arxiv:2104.01180} and two-dimensional Rydberg atomic arrays \cite{arXiv:2104.04119}.
+
 notes:
   - |
     Hardware requirements for implementing surface code QEC can be reduced by utilizing structure in the time slices of the QEC circuits \cite{arxiv:2209.06673}.
@@ -157,20 +162,14 @@ notes:
 
   - 'Review of surface code decoders \cite{arxiv:2307.14989}.'
 
-realizations:
-  - |
-    One cycle of syndrome readout on 19-qubit planar and 24-qubit toric codes realized in two-dimensional Rydberg atomic arrays \cite{arxiv:2112.03923}.
-  - |
-    Signatures of corresponding topological phase of matter detected in superconducting circuits \cite{arxiv:2104.01180} and two-dimensional Rydberg atomic arrays \cite{arXiv:2104.04119}.
-  - |
-    Ground state of the toric code has been implemented with and without twists, and the non-Abelian braiding behavior of the twists, which realize Ising anyons, has been demonstrated \cite{arxiv:2211.09802}.
-
 relations:
   parents:
     - code_id: higher_dimensional_surface
       detail: 'The surface-code CSS stabilizer generator prescription is extendable to higher-dimensional manifolds.'
     - code_id: clifford-deformed_surface
       detail: 'CDSC codes are deformations of the surface code via constant-depth Clifford circuits that may not be CSS.'
+    - code_id: twist_defect_surface
+      detail: 'Twist-defect surface codes reduce to surface codes when there are no defects.'
     - code_id: hypergraph_product
       detail: 'Planar (toric) code can be obtained from hypergraph product of two repetition (cyclic) codes \cite[Ex. 6]{arxiv:1202.0928}.'
     - code_id: lcs