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Improve qml.ppm_compilation to able compile from Clifford+RZ/T into PPR/PPM #2366

@sengthai

Description

@sengthai

Currently, ppm_compilation pass obtains sub-passes such as:

  • qml.transforms.to_ppr
  • qml.transforms.commute_ppr
  • qml.transforms.merge_ppr_ppm
  • qml.transforms.ppr_to_ppm

The new passes have been added, such as gridsynth and decompose_arbitrary_ppr.

Here, we should also include these two passes in the PPM compilation pipeline.
So, the passes' order should be:

  • qml.transforms.to_ppr
  • qml.transforms.decompose_arbitrary_ppr (NEW)
  • qml.transforms.gridsynth (targeting PPR basis) (NEW)
  • qml.transforms.commute_ppr
  • qml.transforms.merge_ppr_ppm
  • qml.transforms.ppr_to_ppm

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