Remove AerCircuit from result of backend.run() (#1845)

* take AerCircuit from _metadata in experiment result

* add reno

* Fix rST formatting

---------

Co-authored-by: Jake Lishman <jake@binhbar.com>

qiskit_aer/backends/aerbackend.py

@@ -458,7 +458,7 @@ def _execute_circuits_job(self, circuits, noise_model, config, job_id="", format
         for result in output["results"]:
             if "header" not in result:
                 continue
-            result["header"]["metadata"] = metadata_map[result["circuit"]]
+            result["header"]["metadata"] = metadata_map[result.pop("circuit")]
 
         # Add execution time
         output["time_taken"] = time.time() - start

releasenotes/notes/remove_aer_circuit_from_metadata-e4fe09029c1a3a3c.yaml

@@ -0,0 +1,5 @@
+---
+fixes:
+  - |
+    Results of ``backend.run()`` were not serializable because they include :class:`.AerCircuit`\ s.
+    This commit makes the results serializable by removing :class:`.AerCircuit`\ s from metadata.

test/terra/backends/aer_simulator/test_circuit.py

@@ -13,6 +13,7 @@
 AerSimulator Integration Tests
 """
 from math import sqrt
+from copy import deepcopy
 from ddt import ddt
 import numpy as np
 from qiskit import ClassicalRegister, QuantumCircuit, QuantumRegister, assemble
@@ -190,7 +191,7 @@ def test_metadata_protected(self):
             self.assertEqual(circuit.metadata["foo"], "bar")
             self.assertEqual(circuit.metadata["object"], object)
 
-        job.result()
+        deepcopy(job.result())
 
     def test_run_qobj(self):
         """Test qobj run"""