Remove get_backend() (#1451)

`Aer.get_backend()` was deprecated as part of the `Provider` abstract
class deprecation in Qiskit/qiskit#12145. This
PR replaces it with instantiating `AerSimulator()` directly so the cron
CI tests can pass again.

---------

Co-authored-by: Will Shanks <[email protected]>

qiskit_experiments/library/quantum_volume/qv_experiment.py

@@ -97,9 +97,9 @@ def __init__(
         self.set_experiment_options(trials=trials, seed=seed)
 
         if not simulation_backend and HAS_AER:
-            from qiskit_aer import Aer
+            from qiskit_aer import AerSimulator
 
-            self._simulation_backend = Aer.get_backend("aer_simulator")
+            self._simulation_backend = AerSimulator()
         else:
             self._simulation_backend = simulation_backend