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ZXCalculusForCAP

The category of ZX-diagrams

2025.08-03

24 August 2025

Mohamed Barakat
Email: mohamed.barakat@uni-siegen.de
Homepage: https://mohamed-barakat.github.io/
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

Fabian Zickgraf
Email: f.zickgraf@dashdos.com
Homepage: https://zickgraf.github.io/
Address:
Walter-Flex-Straße 3
57072 Siegen
Germany

Contents

1 The category of ZX-diagrams

1.1 Constructors

  1.1-1 CategoryOfZXDiagrams
  1.1-2 ZX
  1.1-3 Qubits
  1.1-4 Z_Spider
  1.1-5 X_Spider
  1.1-6 H_Gate
  1.1-7 CategoryOfZXDiagrams_as_CategoryOfCospans_CategoryOfDecoratedQuivers

1.2-1 AsInteger
1.2-2 VertexLabeledGraph

  1.4-1 IsCategoryOfZXDiagrams
  1.4-2 IsObjectInCategoryOfZXDiagrams
  1.4-3 IsMorphismInCategoryOfZXDiagrams

2 The category of cospans

2.1 Constructors

2.1-1 CategoryOfCospans_for_ZXCalculus

  2.2-1 UnderlyingCategory
  2.2-2 UnderlyingObject
  2.2-3 UnderlyingMorphismPair

  2.3-1 IsCategoryOfCospans
  2.3-2 IsCategoryOfCospansObject
  2.3-3 IsCategoryOfCospansMorphism

3.1 Importing and exporting ZX-diagrams

  3.1-1 ExportAsQGraphString
  3.1-2 ExportAsQGraphFile
  3.1-3 ImportFromQGraphString
  3.1-4 ImportFromQGraphFile

4 Precompilation

4.1 Precompiling the category of ZX-diagrams

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