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codes/quantum/categories/string_net/hopf_quantum_double.yml

@@ -12,7 +12,7 @@ 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.
+  The code Hamiltonian is an extension of the quantum double model from groups to Hopf algebras.
   Boundaries of these models have been examined \cite{arxiv:2207.03970,arxiv:2208.06317}.
 
 
@@ -22,7 +22,7 @@ relations:
       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}.
+      detail: 'Extending the Hopf algebra quantum-double construction to a weak Hopf algebra construction yields an alternative formulation \cite{arxiv:1309.4181} for realizing multi-fusion 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}.'
     - code_id: qudit_surface
       detail: 'The modular-qudit surface code can be generalized to a Hopf-algebra quantum-double code whose ground states remain the same but whose excitations are based on quasitriangular semisimple Hopf algebras on \(\mathbb{Z}_q\) \cite{arxiv:2210.07909}.'

codes/quantum/groups/topological/tqd.yml

@@ -29,7 +29,7 @@ relations:
     - code_id: group_quantum
     - code_id: string_net
       detail: 'String-net models reduce to TQDs for categories \(\text{Vec}_G^\omega\), where \(G\) is a finite group, and \(\omega\) is a Type III cocycle.
-      There is also a more direct duality between a large class of string–net models and certain TQD models \cite{arxiv:1211.3695}.'
+      There is a duality between a large class of string–net models and certain TQD models \cite{arxiv:1211.3695}.'
 
 
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