[FTQC][Unified Compiler] Outline MBQC transform

[multiphaseCFD]

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---

Context:

[sc-103563]

The MBQC transform has been outlined in the subroutines in the convert_to_mbqc_formalism pass. This would reduce the number of lines in the IR if the circuit is unrolled.

A few other improvements/considerations:

• Reduced the number of arith.ConstantOp used in defining the measurements.
• The visibility of subroutines are set as private to work better with the symbol-dce pass defined in the catalyst pipeline. Note that current pass inserts subroutines for all gates in the MBQC gate set. This could be redundant if not all gates are applied in a given circuit. However, there is no need to worry about that since the symbol-dce pass would eliminate the unreferenced subroutine given that its visibility is private.
• Note that those subroutines are attached with an attribute mbqc_transform. This attribute is used to skip the convert_to_mbqc_formalism transform for the subroutine (There are "Hadamard" gates in the subroutine, which we don't want to replace it with a subroutine call).
• Note that IfOp in the subroutines could be hitted by the convert_to_mbqc_formalism transform. No need to worry for now as there are no gates in the MBQC gate set there.
• Note that the order of parameters for the subroutine is aligned with the corresponding qml.operation.

Description of the Change:

Benefits:

Take the ncas = 10 (or 21 qubits) XAS circuit ( stateprep ignored), the number of lines of circuit.mlir is 26158, compared to 92185 for the master branch. The number of lines of _llvm.ir.ll is 213173, compared to 420280 for the master branch.

Possible Drawbacks:

Related GitHub Issues:

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.42%. Comparing base (015eb15) to head (2d62ffc).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #8619      +/-   ##
==========================================
- Coverage   99.43%   99.42%   -0.01%     
==========================================
  Files         587      587              
  Lines       61967    61967              
==========================================
- Hits        61615    61613       -2     
- Misses        352      354       +2     

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[joeycarter]

This looks great, thanks @multiphaseCFD! 💯

I don't have much to add, just a few minor things.

[mlxd]

Nice one @multiphaseCFD
Just wondering if we should merge this PR or #8632 first?

Happy to approve based on the answer.

[lillian542]

Thanks, Shuli, this looks great! As well as the reduction in how many lines of IR we’re producing, it also feel his also makes both the IR and the xDSL pass source code easier to read.

I left a couple minor comments, nothing blocking. You may want to coordinate with Sengthai about his PR, I think one of you will have to solve merge conflicts 😅