Add interface to lightning.qubit MCM preprocessing (#760)

**Context:**
Currently blocked by PennyLaneAI/pennylane#5791.
Device preprocessing is being moved inside the ML boundary, so the
interface information needed for correct `hw-like` postselection is
being lost when using `dynamic_one_shot`.

**Description of the Change:**
`qml.devices.preprocess.mid_circuit_measurements` accepts an additional
`interface` kwarg, which is now being used in
`LightningQubit.preprocess`.

**Benefits:**
Expected behaviour with `mcm_method="one-shot"`,
`postselect_mode="hw-like"`, and `jax.jit`.

**Possible Drawbacks:**

**Related GitHub Issues:**

---------

Co-authored-by: ringo-but-quantum <github-ringo-but-quantum@xanadu.ai>
Co-authored-by: Ali Asadi <10773383+maliasadi@users.noreply.github.com>

.github/CHANGELOG.md

@@ -92,6 +92,9 @@
 * `lightning.qubit` and `lightning.kokkos` use `qml.ops.Conditional.base` instead of `qml.ops.Conditional.then_op`.
   [(#752)](https://github.com/PennyLaneAI/pennylane-lightning/pull/752)
 
+* The preprocessing step in `lightning.qubit` now uses interface information to properly support the hardware-like postselection for mid-circuit measurements.
+  [(#760)](https://github.com/PennyLaneAI/pennylane-lightning/pull/760)
+
 * Fix AVX streaming operation support with newer GCC.
   [(#729)](https://github.com/PennyLaneAI/pennylane-lightning/pull/729)
 

pennylane_lightning/core/_version.py

@@ -16,4 +16,4 @@
    Version number (major.minor.patch[-label])
 """
 
-__version__ = "0.37.0-dev34"
+__version__ = "0.37.0-dev35"

pennylane_lightning/lightning_qubit/lightning_qubit.py

@@ -582,7 +582,10 @@ def preprocess(self, execution_config: ExecutionConfig = DefaultExecutionConfig)
         program.add_transform(validate_observables, accepted_observables, name=self.name)
         program.add_transform(validate_device_wires, self.wires, name=self.name)
         program.add_transform(
-            mid_circuit_measurements, device=self, mcm_config=exec_config.mcm_config
+            mid_circuit_measurements,
+            device=self,
+            mcm_config=exec_config.mcm_config,
+            interface=exec_config.interface,
         )
         program.add_transform(
             decompose,

tests/new_api/test_device.py

@@ -287,7 +287,7 @@ def test_preprocess(self, adjoint):
         expected_program.add_transform(validate_observables, accepted_observables, name=device.name)
         expected_program.add_transform(validate_device_wires, device.wires, name=device.name)
         expected_program.add_transform(
-            mid_circuit_measurements, device=device, mcm_config=MCMConfig()
+            mid_circuit_measurements, device=device, mcm_config=MCMConfig(), interface=None
         )
         expected_program.add_transform(
             decompose,