diff --git a/qiskit/providers/aer/aerprovider.py b/qiskit/providers/aer/aerprovider.py
index 31f1f900b5..7846b897bc 100644
--- a/qiskit/providers/aer/aerprovider.py
+++ b/qiskit/providers/aer/aerprovider.py
@@ -21,6 +21,7 @@
 from .backends.statevector_simulator import StatevectorSimulator
 from .backends.unitary_simulator import UnitarySimulator
 from .backends.pulse_simulator import PulseSimulator
+from .profile import optimize_backend_options
 
 
 class AerProvider(BaseProvider):
@@ -56,6 +57,5 @@ def __str__(self):
     @staticmethod
     def optimize_backend_options(min_qubits=10, max_qubits=20, ntrials=10):
         """Set optimal OpenMP and fusion options for backend."""
-        from .profile import optimize_backend_options
         return optimize_backend_options(
             min_qubits=min_qubits, max_qubits=max_qubits, ntrials=ntrials)
diff --git a/qiskit/providers/aer/backends/aerbackend.py b/qiskit/providers/aer/backends/aerbackend.py
index b2198cc6a1..80fdec4e80 100644
--- a/qiskit/providers/aer/backends/aerbackend.py
+++ b/qiskit/providers/aer/backends/aerbackend.py
@@ -237,14 +237,21 @@ def _run_job(self, job_id, qobj, backend_options, noise_model, validate):
         # Add default OpenMP options
         if 'statevector_parallel_threshold' not in backend_options and hasattr(
                 self, '_statevector_parallel_threshold'):
-            backend_options['statevector_parallel_threshold'] = self._statevector_parallel_threshold
+            backend_options['statevector_parallel_threshold'] = \
+                getattr(self, '_statevector_parallel_threshold')
 
         # Add default fusion options
         attr_postfix = '_gpu' if 'gpu' in backend_options.get('method', '') else ''
         if 'fusion_threshold' not in backend_options and hasattr(
-            self, f'_fusion_threshold{attr_postfix}'):
+                self, f'_fusion_threshold{attr_postfix}'):
             # Set fusion threshold
             backend_options['fusion_threshold'] = getattr(self, f'_fusion_threshold{attr_postfix}')
+        for i in range(1, 6):
+            if f'fusion_cost.{i}' not in backend_options and \
+               hasattr(self, f'_fusion_cost{attr_postfix}.{i}'):
+                # Set cost for each
+                backend_options[f'fusion_cost.{i}'] = getattr(self,
+                                                              f'_fusion_cost{attr_postfix}.{i}')
 
         # The new function swaps positional args qobj and job id so we do a
         # type check to swap them back
diff --git a/qiskit/providers/aer/profile.py b/qiskit/providers/aer/profile.py
index b1e0d17e64..ecbc9b85fb 100644
--- a/qiskit/providers/aer/profile.py
+++ b/qiskit/providers/aer/profile.py
@@ -13,7 +13,10 @@
 Profile backend options for optimal performance
 """
 from qiskit import transpile, assemble, execute
+from qiskit.circuit.library import QuantumVolume
 from .aererror import AerError
+from .backends.aerbackend import AerBackend
+from .backends.qasm_simulator import QasmSimulator
 
 
 def optimize_backend_options(min_qubits=10, max_qubits=20, ntrials=10):
@@ -49,8 +52,6 @@ def optimize_backend_options(min_qubits=10, max_qubits=20, ntrials=10):
     # TODO: Write profile to a local qiskitaerrc file so this doesn't
     # need to be re-run on a system and the following can be loaded
     # in the AerBackend class from the rc file if it is found
-    from qiskit.providers.aer.backends.aerbackend import AerBackend
-
     if 'statevector_parallel_threshold' in profile:
         AerBackend._statevector_parallel_threshold = profile[
             'statevector_parallel_threshold']
@@ -66,9 +67,6 @@ def profile_parallel_threshold(min_qubits=10, max_qubits=20, ntrials=10,
                                backend_options=None,
                                return_ratios=False):
     """Evaluate optimal OMP parallel threshold for current system."""
-    from qiskit.circuit.library import QuantumVolume
-    from qiskit.providers.aer.backends.qasm_simulator import QasmSimulator
-
     simulator = QasmSimulator()
     opts = {'method': 'statevector',
             'max_parallel_experiments': 1,
@@ -92,10 +90,10 @@ def profile_parallel_threshold(min_qubits=10, max_qubits=20, ntrials=10,
         for val in [i - 1, i]:
             opts['statevector_parallel_threshold'] = val
             result = simulator.run(qobj, backend_options=opts).result()
-            t = 0.0
+            time_taken = 0.0
             for j in range(ntrials):
-                t += result.results[j].time_taken
-            times.append(t)
+                time_taken += result.results[j].time_taken
+            times.append(time_taken)
 
         # Compute ratio
         ratio = times[1] / times[0]
@@ -123,9 +121,6 @@ def profile_fusion_threshold(min_qubits=10, max_qubits=20, ntrials=10,
                              backend_options=None, gpu=False,
                              return_ratios=False):
     """Evaluate optimal OMP parallel threshold for current system."""
-    from qiskit.circuit.library import QuantumVolume
-    from qiskit.providers.aer.backends.qasm_simulator import QasmSimulator
-
     simulator = QasmSimulator()
     opts = {'method': 'statevector',
             'max_parallel_experiments': 1,
@@ -157,10 +152,10 @@ def profile_fusion_threshold(min_qubits=10, max_qubits=20, ntrials=10,
         for val in [i, i + 1]:
             opts['fusion_threshold'] = val
             result = simulator.run(qobj, backend_options=opts).result()
-            t = 0.0
+            time_taken = 0.0
             for j in range(ntrials):
-                t += result.results[j].time_taken
-            times.append(t)
+                time_taken += result.results[j].time_taken
+            times.append(time_taken)
 
         # Compute ratio
         ratio = times[1] / times[0]