Fix handling of cumulative_angles in merge_rotations (#7011)

**Context:**

For the `Rot` gate, the angles can cancel in a non-trivial way (e.g.
Rot(φ,0,-φ) = RZ(φ) RY(0) RZ(-φ) = RZ(0) = I).

Unlike `single_qubit_fusion`, this was not being handled correctly and
only the trivial case where all angles are zero was being checked.

**Description of the Change:**

- Create a boolean flag `angles_cancel` that determines whether the
operator is the identity and can be ignored in the transformed tape.
- Added a test to cover the use case.

**Benefits:** Correct behaviour.

**Possible Drawbacks:** None identified.

**Related GitHub Issues:** Fixes
#7010

[sc-85327]

---------

Co-authored-by: David Wierichs <[email protected]>
Co-authored-by: Christina Lee <[email protected]>

doc/releases/changelog-dev.md

@@ -42,6 +42,9 @@
 
 <h3>Improvements 🛠</h3>
 
+* `merge_rotations` now correctly simplifies merged `qml.Rot` operators whose angles yield the identity operator.
+  [(#7011)](https://github.com/PennyLaneAI/pennylane/pull/7011)
+
 * Bump `rng_salt` to `v0.40.0`.
   [(#6854)](https://github.com/PennyLaneAI/pennylane/pull/6854)
 

pennylane/transforms/optimization/merge_rotations.py

@@ -177,6 +177,7 @@ def stop_at(obj):
 
         # We need to use stack to get this to work and be differentiable in all interfaces
         cumulative_angles = qml.math.stack(current_gate.parameters)
+        angles_cancel = False
         interface = qml.math.get_interface(cumulative_angles)
         # As long as there is a valid next gate, check if we can merge the angles
         while next_gate_idx is not None:
@@ -194,9 +195,16 @@ def stop_at(obj):
                 # The Rot gate must be treated separately
                 if isinstance(current_gate, qml.Rot):
                     cumulative_angles = fuse_rot_angles(cumulative_angles, next_params)
+                    # For the Rot gate, the angles can cancel in a non-trivial way
+                    # e.g. Rot(φ,0,-φ) = RZ(φ) RY(0) RZ(-φ) = RZ(0) = I.
+                    test_angles = qml.math.stack(
+                        [cumulative_angles[0] + cumulative_angles[2], cumulative_angles[1]]
+                    )
                 # Other, single-parameter rotation gates just have the angle summed
                 else:
                     cumulative_angles = cumulative_angles + next_params
+                    test_angles = cumulative_angles
+                angles_cancel = qml.math.allclose(test_angles, 0.0, atol=atol, rtol=0)
             # If it is not, we need to stop
             else:
                 break
@@ -210,7 +218,7 @@ def stop_at(obj):
         if (
             qml.math.is_abstract(cumulative_angles)
             or qml.math.requires_grad(cumulative_angles)
-            or not qml.math.allclose(cumulative_angles, 0.0, atol=atol, rtol=0)
+            or not angles_cancel
         ):
             with QueuingManager.stop_recording():
                 new_operations.append(

tests/transforms/test_optimization/test_merge_rotations.py

@@ -55,6 +55,17 @@ def qfunc():
             assert op_obtained.name == op_expected.name
             assert np.allclose(op_obtained.parameters, op_expected.parameters)
 
+    def test_rot_gate_cancel(self):
+        """Test that two rotation gates get merged to the identity operator (cancel)."""
+
+        def qfunc():
+            qml.Rot(-1, 0, 1, wires=0)
+            qml.Rot(-1, 0, 1, wires=0)
+
+        transformed_qfunc = merge_rotations(qfunc)
+        ops = qml.tape.make_qscript(transformed_qfunc)().operations
+        assert not ops
+
     @pytest.mark.parametrize(
         ("theta_1", "theta_2", "expected_ops"),
         [