diff --git a/qiskit/utils/backend_utils.py b/qiskit/utils/backend_utils.py
index 7f71a7c91897..df89d7f194da 100644
--- a/qiskit/utils/backend_utils.py
+++ b/qiskit/utils/backend_utils.py
@@ -181,16 +181,21 @@ def is_statevector_backend(backend):
     Returns:
         bool: True is statevector
     """
+    if backend is None:
+        return False
+    backend_interface_version = _get_backend_interface_version(backend)
     if has_aer():
         from qiskit.providers.aer.backends import AerSimulator, StatevectorSimulator
 
         if isinstance(backend, StatevectorSimulator):
             return True
-        if isinstance(backend, AerSimulator) and "aer_simulator_statevector" in backend.name():
-            return True
-    if backend is None:
-        return False
-    backend_interface_version = _get_backend_interface_version(backend)
+        if isinstance(backend, AerSimulator):
+            if backend_interface_version <= 1:
+                name = backend.name()
+            else:
+                name = backend.name
+            if "aer_simulator_statevector" in name:
+                return True
     if backend_interface_version <= 1:
         return backend.name().startswith("statevector")
     else:
diff --git a/releasenotes/notes/fix_backend_name-e84661707058b529.yaml b/releasenotes/notes/fix_backend_name-e84661707058b529.yaml
new file mode 100644
index 000000000000..ed0cbe9a2658
--- /dev/null
+++ b/releasenotes/notes/fix_backend_name-e84661707058b529.yaml
@@ -0,0 +1,7 @@
+---
+fixes:
+  - |
+    Fixed an issue in the :class:`.QuantumInstance` class where it was assuming
+    all ``AerSimulator`` backends were always :class:`.BackendV1`. This would cause
+    combatibility issues with the 0.13.0 release of ``qiskit-aer`` which is starting to
+    use :class:`.BackendV2` for `AerSimulator`` backends.