PyZX as a pattern optimization backend?

[shinich1]

Is your feature request related to a problem? Please describe.
na

Describe the feature you'd like
Implement pyzx interface to use ZX-calculus as a pattern optimization backend. This means we will need to construct graph-like diagram, optimize with pyZX, and then get pattern out of it to be simulated or executed on device.

Additional context
https://quantum-journal.org/papers/q-2021-03-25-421/
https://arxiv.org/pdf/2304.08166.pdf
etc

[king-p3nguin]

Note that PyZX is now updating the function to_graph_like. The current version's to_graph_like function does not work, so we may need to wait for the next release (or implement it ourselves).
zxcalc/pyzx#189

Getting a pattern out of the PyZX diagram can be done by graphix.generator.generate_from_graph().