[WIP] Added loop boundary optimization pass

[sengthai]

Context:

The Loop Boundary Optimization identifies and optimizes redundant quantum operations that occur at loop iteration boundaries, where operations at iteration boundaries often cancel each other out.

This method is standalone pass but also integrated in merge rotation and cancel inverses pass.

It specifically targets:

1. Pattern recognition: Identifies matching quantum operations at the beginning and end of loop iteration.
2. Operation Hoisting:
   • Moves matching operations from loop boundaries to outside loop
   • Top-edge and operations are hoisted before the loop and after the loop, respectively.

Description of the Change:

• Register new pass for loop boundary optimization
• Implement to support this method on merge_rotation and cancel_inverses pass

Benefits:

• Eliminates redundant operations that cancel each other between iterations
• Reduces quantum circuit depth and gate count
• Effective for compute/uncompute patters in loops

Limited Scope

• Only works with perfectly matching operations
  • Support gates: Pauli gates, H gate, CNOT, and rotation gates.

Possible Drawbacks:

• Increased compilation time

[sc-83037]

[github-actions]

Hello. You may have forgotten to update the changelog!
Please edit doc/releases/changelog-dev.md on your branch with:

• A one-to-two sentence description of the change. You may include a small working example for new features.
• A link back to this PR.
• Your name (or GitHub username) in the contributors section.

[dime10]

Nice work so far! I left a few comments regarding the foundations of the pass, but since it's still a work in progress I didn't look at the code too closely yet :)

[dime10]

This doesn't have to be solved now, but I do think in the future we'll want a single pass that applies many quantum peephole optimizations, similarly to the canonicalize pass in MLIR. That way, we can actually make use of the fixed-point greedy pattern applicator, taking advantage of one peephole optimization enabling another.

[paul0403]

Remember to link to the shortcut story! You can see how this is done on other PRs :D

[sengthai]

Remember to link to the shortcut story! You can see how this is done on other PRs :D

Of course, will do. Thanks Paul!