ZXdb: ZX-calculus on graph databases

This implementation provides the core simplification rules from PyZX implemented as openCypher queries:

• Spider fusion
• Identity removal
• Local complementation
• Gadget fusion
• Pivot rule
• Pivot gadget rule
• Pivot boundary rule
• Bialgebra simplification

Queries can be found from query_collections folder. It is easiest to install Memgraph and import the collections to Memgraph Lab. Then one can demonstrate the usage of the platform with the instances that are in the test folder.

This package also translates ZX-diagrams into Quimb tensor networks. It seems like this way, one can simulate a lot larger diagrams than with the tensor networks in PyZX. For this, see demo_quimb.ipynb.

Styles for MemGraph Lab

Apply the following style definitions in MemGraph Leb to match the style with PyZX:

@NodeStyle Equals(Property(node, "t"), 0) {
  color: #000000
  color-hover: #000000
  color-selected: #000000
}

@NodeStyle Equals(Property(node, "t"), 1) {
  color: #d6fccf
  color-hover: #d6fccf
  color-selected: #d6fccf
}

@NodeStyle Equals(Property(node, "t"), 2) {
  color: #f0908a
  color-hover: #f0908a
  color-selected: #f0908a
}

@NodeStyle Equals(Property(node, "t"), 3) {
  color: #ffd700
  color-hover: #ffd700
  color-selected: #ffd700
}

Notes on differences compared to PyZX:

• There is possibility to perform spider fusion when red and green spider are connected with a Hadamard edge. As far as I know, spider_simp in PyZX does not detect these cases. Evaluating these cases is not implemented but it is noted.
• Bialg_simp is not clearly explained in the PyZX. I understand that it is the ''inverse'' of the bialgebra rule applied to all non-interacting instances.
• gadget_simp might have some side effects that depend on the phases?