Fix init of EstimatorV2 and SamplerV2 (Qiskit#2120)

* fix init of EstimatorV2 and SamplerV2 to handle method

* add release note

* fix from_backend and example in README

* remove setting density_matrix

README.md

@@ -134,13 +134,13 @@ provider = QiskitRuntimeService(channel='ibm_quantum', token="set your own token
 backend = provider.get_backend("ibm_kyoto")
 
 # create sampler from the actual backend
-sampler.from_backend(backend)
+sampler = SamplerV2.from_backend(backend)
 
 # run a sampler job on the parameterized circuits with noise model of the actual hardware
-job3 = sampler.run([(pqc, theta1), (pqc2, theta2)])
+bell_t = transpile(bell, AerSimulator(basis_gates=["ecr", "id", "rz", "sx"]), optimization_level=0)
+job3 = sampler.run([bell_t], shots=128)
 job_result = job3.result()
-print(f"Parameterized for Bell circuit w/noise: {job_result[0].data.meas.get_counts()}")
-
+print(f"counts for Bell circuit w/noise: {job_result[0].data.meas.get_counts()}")
 ```
 
 ## Contribution Guidelines

qiskit_aer/primitives/estimator_v2.py

@@ -70,12 +70,14 @@ 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)
-
-    def from_backend(self, backend, **options):
-        """use external backend"""
-        self._backend.from_backend(backend, **options)
+        self._backend = AerSimulator(**self.options.backend_options)
+
+    @classmethod
+    def from_backend(cls, backend, **options):
+        """make new sampler that uses external backend"""
+        estimator = cls(**options)
+        estimator._backend = AerSimulator.from_backend(backend)
+        return estimator
 
     @property
     def options(self) -> Options:

qiskit_aer/primitives/sampler_v2.py

@@ -100,9 +100,12 @@ def __init__(
         self._options = Options(**options) if options else Options()
         self._backend = AerSimulator(**self.options.backend_options)
 
-    def from_backend(self, backend, **options):
-        """use external backend"""
-        self._backend.from_backend(backend, **options)
+    @classmethod
+    def from_backend(cls, backend, **options):
+        """make new sampler that uses external backend"""
+        sampler = cls(**options)
+        sampler._backend = AerSimulator.from_backend(backend)
+        return sampler
 
     @property
     def default_shots(self) -> int:

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