Transform to convert to MBQC formalism

[lillian542]

Context:

We have a transform to go from an arbitrary circuit to the gateset compatible with textbook MBQC. Now we want to convert that the MBQC formalism, expressed using resource states, parametrized MCMs and byproduct corrections.

Description of the Change:

We add a transform that performs a simple conversion from that gate-set to the MBQC formalism. "Simple" here means:

• No consolidation of Pauli operations and/or byproduct operations
• Byproducts are applied online after each measurement protocol is complete, no offline corrections
• we use the qubit manager to allocate qubits on the tape before execution (not capture compatible, we unroll all program structure)

This is a very direct, naive conversion to the MBQC formalism. But it does the thing, so it's a good place to start - and we can use it as a baseline for quantifying future improvements in our circuit conversion.

Benefits:
We can convert a circuit to a simple, un-optimized implementation of the same circuit in the MBQC formalism.

[sc-88533]

[JerryChen97]

This might help, though ugly
P.S. no it didn't

[mlxd]

Great job @lillian542
Nothing further from me

[joeycarter]

Looks good! 🎉

[JerryChen97]

LGTM! Just one more good-to-have comment.

[multiphaseCFD]

Thanks @lillian542 for the nice work. Just wondering why qml.math is preferred over qml.numpy or numpy here.