Update rewrites to work well with Multigraphs

[boldar99]

Basic rewrites that need to be fixed:

• [x] Color change
• [x] Fusion of multiple vertices
• [x] Fusion sometimes with a mulit-edge
• [x] Push Pauli
• [x] Matching ID crashes ZXLive if one of the edges is a multi-edge
• [x] Bialgebra
• [x] Copy 0/pi spider
• [x] Magic wand

[RazinShaikh]

These are mostly issues in PyZX so maybe you should create an issue there as well?

[RazinShaikh]

Most basic rewrites are fixed now but a many others are still broken. We should fix the graph-like rules next:

• [ ] local complementation
• [ ] pivot (@colltoaction)
• [ ] boundary pivot
• [ ] gadget pivot
• [ ] fuse phase gadget
• [ ] supplementarity

For example, pivot incorrectly gives the following diagram with parallel edges

[jvdwetering]

Is that example incorrect? Do you want it to remove the parallel edges?

[RazinShaikh]

It should remove parallel edges. The rightmost edge should be removed so that's also wrong.

[jvdwetering]

That edge only belongs to the neighbourset of the right-pivoted vertex, so that one should stay, right? I think these diagrams are semantically correct, just that you would want the pivot to actually complement the edge set, i.e. by applying some general Hopf rule afterwards.

[colltoaction]

There is an exception unpacking a tuple that is suppressed during this rewrite.

  File "/home/mcoll/.local/lib/python3.11/site-packages/pyzx/graph/multigraph.py", line 240, in remove_edge
    s,t,ty = edge
    ^^^^^^
ValueError: not enough values to unpack (expected 3, got 2)

[jvdwetering]

Some discussion on how this can be implemented for the graph-like rewrites:

• A graph-like rewrite should only match if the vertices it matches on form a simple graph. This is to prevent confusion about the intended behaviour when there are parallel edges between neighbours when doing for instance local complementation. In other words: graph-like rewrites only match to parts of the diagram that are graph-like, and by definition these do not have parallel edges.
• A way to implement the correct rewrite is to to store the value of get_auto_simplify, and then set it to True for the duration of the rewrite, to automatically get rid of parallel edges.