[Capture] First PR for enabling dynamic decompositions with PLxPR enabled

doc/releases/changelog-dev.md

@@ -88,13 +88,6 @@
                   convert_to_numpy=True)
   ```
 
-* The higher order primitives in program capture can now accept inputs with abstract shapes.
-  [(#6786)](https://github.com/PennyLaneAI/pennylane/pull/6786)
-
-* The `PlxprInterpreter` classes can now handle creating dynamic arrays via `jnp.ones`, `jnp.zeros`,
-  `jnp.arange`, and `jnp.full`.
-  [#6865)](https://github.com/PennyLaneAI/pennylane/pull/6865)
-
 * `QNode` objects now have an `update` method that allows for re-configuring settings like `diff_method`, `mcm_method`, and more. This allows for easier on-the-fly adjustments to workflows. Any arguments not specified will retain their original value.
   [(#6803)](https://github.com/PennyLaneAI/pennylane/pull/6803)
 
@@ -154,6 +147,20 @@
 * The `qml.clifford_t_decomposition` has been improved to use less gates when decomposing `qml.PhaseShift`.
   [(#6842)](https://github.com/PennyLaneAI/pennylane/pull/6842)
 
+
+<h4>Capturing and representing hybrid programs</h4>
+
+* Implemented a `compute_plxpr_decomposition` method in the `qml.operation.Operator` class to apply dynamic decompositions
+  with program capture enabled.
+  [(#6859)](https://github.com/PennyLaneAI/pennylane/pull/6859)
+
+* The higher order primitives in program capture can now accept inputs with abstract shapes.
+  [(#6786)](https://github.com/PennyLaneAI/pennylane/pull/6786)
+
+* The `PlxprInterpreter` classes can now handle creating dynamic arrays via `jnp.ones`, `jnp.zeros`,
+  `jnp.arange`, and `jnp.full`.
+  [#6865)](https://github.com/PennyLaneAI/pennylane/pull/6865)
+
 <h3>Breaking changes 💔</h3>
 
 * `MultiControlledX` no longer accepts strings as control values.

pennylane/operation.py

@@ -1349,6 +1349,33 @@ def compute_decomposition(
         """
         raise DecompositionUndefinedError
 
+    @classproperty
+    def has_plxpr_decomposition(cls) -> bool:
+        """Whether or not the Operator returns a defined plxpr decomposition."""
+        return cls.compute_plxpr_decomposition != Operator.compute_plxpr_decomposition
+
+    @staticmethod
+    def compute_plxpr_decomposition(*args, **hyperparameters) -> None:
+        r"""Experimental method to compute the dynamic decomposition of the operator with program capture enabled.
+
+        When the program capture feature is enabled with ``qml.capture.enable()``, the decomposition of the operator
+        is computed with this method if it is defined. Otherwise, the :meth:`~.Operator.compute_decomposition` method is used.
+
+        If this method is defined, the control flow operations within the method are recorded in the JAX representation
+        of the operator's decomposition.
+
+        This method is experimental and subject to change.
+
+        .. seealso:: :meth:`~.Operator.compute_decomposition`.
+
+        Args:
+            *args (list): positional arguments passed to the operator, including trainable parameters and wires
+            **hyperparameters (dict): non-trainable hyperparameters of the operator, as stored in the ``hyperparameters`` attribute
+
+        """
+
+        raise DecompositionUndefinedError
+
     # pylint: disable=no-self-argument, comparison-with-callable
     @classproperty
     def has_diagonalizing_gates(cls) -> bool:

pennylane/transforms/decompose.py

@@ -157,7 +157,18 @@ def interpret_operation_eqn(self, eqn):
             with qml.QueuingManager.stop_recording():
                 op = eqn.primitive.impl(*invals, **eqn.params)
             if eqn.outvars[0].__class__.__name__ == "DropVar":
-                return self.decompose_operation(op)
+
+                if op.has_plxpr_decomposition:
+
+                    args = (*op.parameters, *op.wires)
+                    qml.capture.run_autograph(op.compute_plxpr_decomposition)(
+                        *args, **op.hyperparameters
+                    )
+
+                else:
+
+                    return self.decompose_operation(op)
+
             return op
 
     # pylint: disable=unused-variable,missing-function-docstring