Fix serialization of primitives (#9076) (#9152)

* fix serialization of primitives

* Update releasenotes/notes/fix-serialization-primitives-c1e44a37cfe7a32a.yaml

Co-authored-by: Matthew Treinish <mtreinish@kortar.org>

* rm tests

* Update releasenotes/notes/fix-serialization-primitives-c1e44a37cfe7a32a.yaml

Co-authored-by: Matthew Treinish <mtreinish@kortar.org>

Co-authored-by: Matthew Treinish <mtreinish@kortar.org>
(cherry picked from commit a4a6be0)

Co-authored-by: Ikko Hamamura <ikkoham@users.noreply.github.com>

qiskit/primitives/backend_estimator.py

@@ -147,6 +147,9 @@ def __new__(  # pylint: disable=signature-differs
         self = super().__new__(cls)
         return self
 
+    def __getnewargs__(self):
+        return (self._backend,)
+
     @property
     def transpile_options(self) -> Options:
         """Return the transpiler options for transpiling the circuits."""

qiskit/primitives/backend_sampler.py

@@ -23,10 +23,10 @@
 from qiskit.result import QuasiDistribution, Result
 from qiskit.transpiler.passmanager import PassManager
 
+from .backend_estimator import _prepare_counts, _run_circuits
 from .base import BaseSampler, SamplerResult
 from .primitive_job import PrimitiveJob
 from .utils import _circuit_key
-from .backend_estimator import _run_circuits, _prepare_counts
 
 
 class BackendSampler(BaseSampler):
@@ -83,6 +83,9 @@ def __new__(  # pylint: disable=signature-differs
         self = super().__new__(cls)
         return self
 
+    def __getnewargs__(self):
+        return (self._backend,)
+
     @property
     def preprocessed_circuits(self) -> list[QuantumCircuit]:
         """

releasenotes/notes/fix-serialization-primitives-c1e44a37cfe7a32a.yaml

@@ -0,0 +1,8 @@
+---
+fixes:
+  - |
+    Fixed an issue with the primitive classes, :class:`~.BackendSampler` and :class:`~.BackendEstimator`,
+    where instances were not able to be serialized with ``pickle``. In general these classes are not guaranteed
+    to be serializable as :class:`~.BackendV2` and :class:`~.BackendV1` instances are not required to be
+    serializable (and often are not), but the class definitions of :class:`~.BackendSampler` and
+    :class:`~.BackendEstimator` no longer prevent the use of ``pickle``.

test/python/primitives/test_estimator.py

@@ -13,9 +13,9 @@
 """Tests for Estimator."""
 
 import unittest
-from ddt import ddt, data, unpack
 
 import numpy as np
+from ddt import data, ddt, unpack
 
 from qiskit.circuit import Parameter, QuantumCircuit
 from qiskit.circuit.library import RealAmplitudes