hopf algebra QD

errorcorrectionzoo · Apr 27, 2024 · 9bfacfd · 9bfacfd
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diff --git a/...uantum/categories/enriched_string_net.yml → ...gories/string_net/enriched_string_net.yml b/...uantum/categories/enriched_string_net.yml → ...gories/string_net/enriched_string_net.yml
diff --git a/codes/quantum/categories/fibonacci.yml → ...antum/categories/string_net/fibonacci.yml b/codes/quantum/categories/fibonacci.yml → ...antum/categories/string_net/fibonacci.yml
diff --git a/...s/quantum/categories/groupoid_surface.yml → ...ategories/string_net/groupoid_surface.yml b/...s/quantum/categories/groupoid_surface.yml → ...ategories/string_net/groupoid_surface.yml
diff --git a/codes/quantum/categories/string_net/hopf_quantum_double.yml b/codes/quantum/categories/string_net/hopf_quantum_double.yml
@@ -0,0 +1,34 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: hopf_quantum_double
+physical: categories
+logical: categories
+
+name: 'Hopf-algebra quantum-double code'
+introduced: '\cite{arxiv:1007.5283,arxiv:1206.2308}'
+
+description: |
+  Code whose codewords realize 2D gapped topological order defined by a Hopf algebra \(H\).
+  The code Hamiltonian is an extension of the quantum double model from groups to to Hopf algebras.
+
+
+relations:
+  parents:
+    - code_id: string_net
+      detail: 'String-net models reduce to Hopf-algebra quantum-double codes for categories \(\text{Rep}(H)\), where \(H\) is a Hopf algebra \cite{arxiv:1206.2308}.'
+  cousins:
+    - code_id: enriched_string_net
+      detail: 'Extending the Hopf algebra quantum-double construction to a weak Hopf algebra construction yields an alternative formulation \cite{arxiv:1309.4181} for realizing enriched string-net topological orders because of the relationship between representations of weak Hopf algebras and multi-fusion categories \cite{arXiv:math/0203060}.
+      Tensor network constructions can be done for either formulation \cite{arxiv:2204.05940}.'
+
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-04-27'
diff --git a/codes/quantum/categories/string_net.yml → ...ntum/categories/string_net/string_net.yml b/codes/quantum/categories/string_net.yml → ...ntum/categories/string_net/string_net.yml
diff --git a/codes/quantum/groups/topological/quantum_double.yml b/codes/quantum/groups/topological/quantum_double.yml
@@ -46,7 +46,10 @@ relations:
     - code_id: group_gkp
       detail: 'Quantum-double Hamiltonians can be expressed in terms of \(X\)- and \(Z\)-type operators of group-GKP codes; see \cite[Sec. 3.3]{arxiv:2111.12096}.'
     - code_id: tqd
-      detail: 'The anyon theory corresponding to a quantum-double code is a TQD with trivial cocycle. These models realize local topological order (LTO) \cite{arxiv:2309.13440}.'
+      detail: 'The anyon theory corresponding to a quantum-double code is a TQD with trivial cocycle.
+      These models realize local topological order (LTO) \cite{arxiv:2309.13440}.'
+    - code_id: hopf_quantum_double
+      detail: 'Hopf-algebra quantum-double codes reduce to quantum-double codes when the Hopf algebra is a \hyperref[topic:group-algebra]{group algebra}.'
 
 
 # Begin Entry Meta Information

diff --git a/codes/quantum/groups/topological/tqd.yml b/codes/quantum/groups/topological/tqd.yml
@@ -23,7 +23,7 @@ description: |
 features:
   encoders:
     - 'For any solvable group \(G\), ground-state preparation can be done with an adaptive constant-depth circuit with geometrically local gates and measurements throughout \cite{arxiv:2209.06202}.'
-    
+
 relations:
   parents:
     - code_id: group_quantum