Adding deprecation warnings for new noise learner format (Qiskit#1848)

* json

* warnings

* revert

* 0.27.0

* release

qiskit_ibm_runtime/utils/noise_learner_result.py

@@ -21,6 +21,8 @@
 from qiskit.circuit import QuantumCircuit
 from qiskit.quantum_info import PauliList
 
+from ..utils.deprecation import issue_deprecation_msg
+
 
 class PauliLindbladError:
     r"""A Pauli error channel generated by a Pauli Lindblad dissipators.
@@ -136,6 +138,32 @@ def error(self) -> PauliLindbladError:
         """
         return self._error
 
+    @property
+    def generators(self) -> PauliList:
+        r"""
+        (DEPRECATED) The Pauli Lindblad generators of the error channel in this :class:`.~LayerError`.
+        """
+        issue_deprecation_msg(
+            "The ``generators`` property is deprecated",
+            "0.27.0",
+            "Instead, you can access the generators through the ``error`` property.",
+            1,
+        )
+        return self.error.generators
+
+    @property
+    def rates(self) -> NDArray[np.float64]:
+        r"""
+        (DEPRECATED) The Lindblad generator rates of the error channel in this :class:`.~LayerError`.
+        """
+        issue_deprecation_msg(
+            "The ``rates`` property is deprecated",
+            "0.27.0",
+            "Instead, you can access the rates through the ``error`` property.",
+            1,
+        )
+        return self.error.rates
+
     @property
     def num_qubits(self) -> int:
         r"""

release-notes/unreleased/1844.feat.rst

@@ -0,0 +1 @@
+Added ``PauliLindbladError`` and ``LayerError`` classes to represent layers noise processes.