✨ Add canonicalization pattern for DCX inverse cancellation in QCO dialect

[burgholzer]

Description

Add a canonicalization pattern to eliminate redundant DCX operations in the QCO dialect. A DCX operation followed by a DCX operation with swapped targets is equivalent to the identity and can be removed.

Background

The DCX (double-controlled-X) gate's inverse is the DCX gate with swapped targets. This means:

• DCX(q0, q1) followed by DCX(q1, q0) cancels out

Proposed Solution

Implement a canonicalization pattern similar to the existing patterns for SWAP and ECR operations that:

1. Detects consecutive DCX operations with swapped targets
2. Removes both operations by replacing with pass-through qubits

References

• Follow-up from PR #1264: 🗺️ MLIR Dialect Redesign #1264 (comment)
• Similar patterns exist in:
  • mlir/lib/Dialect/QCO/IR/Operations/StandardGates/SWAPOp.cpp
  • mlir/lib/Dialect/QCO/IR/Operations/StandardGates/ECROp.cpp

Implementation Location

The pattern should be added in mlir/lib/Dialect/QCO/IR/Operations/StandardGates/DCXOp.cpp and hasCanonicalizer = 1 should be added to DCXOp in mlir/include/mlir/Dialect/QCO/IR/QCOOps.td.
Labels: enhancement, MLIR
Assignee: burgholzer