Fix init of EstimatorV2 and SamplerV2

qiskit_aer/primitives/estimator_v2.py

@@ -70,8 +70,13 @@ def __init__(
                 the runtime options (``run_options``).
         """
         self._options = Options(**options) if options else Options()
-        method = "density_matrix" if "noise_model" in self.options.backend_options else "automatic"
-        self._backend = AerSimulator(method=method, **self.options.backend_options)
+        if "method" not in self.options.backend_options:
+            method = (
+                "density_matrix" if "noise_model" in self.options.backend_options else "automatic"
+            )
+            ops = dict(method=method)
+            self.options.backend_options.update(ops)
+        self._backend = AerSimulator(**self.options.backend_options)
 
     def from_backend(self, backend, **options):
         """use external backend"""

qiskit_aer/primitives/sampler_v2.py

@@ -98,6 +98,12 @@ def __init__(
         self._seed = seed
 
         self._options = Options(**options) if options else Options()
+        if "method" not in self.options.backend_options:
+            method = (
+                "density_matrix" if "noise_model" in self.options.backend_options else "automatic"
+            )
+            ops = dict(method=method)
+            self.options.backend_options.update(ops)
         self._backend = AerSimulator(**self.options.backend_options)
 
     def from_backend(self, backend, **options):

releasenotes/notes/fix_primitiveV2_init-afe7b331ddbef538.yaml

@@ -0,0 +1,5 @@
+---
+fixes:
+  - |
+    Fixed init function of EstimatorV2 and SamplerV2 to set `method` in
+    its option property if there is no `method` in input parameter