Fix Renew example codes in README Qiskit#1806: qiskit.providers.ibmq …

…is deprecated; ibmq_athens is not available (Qiskit#1831)

* Fix REAM Qiskit#1896 qiskit.providers.ibmq is deprecated;

* In README example, simplify code to get aersim_backend

* Update README.md remove shots=1000

* use FakeManilaV2

* Update README.md import Fake backend in the beginning

* Update README.md remove unneeded IBM_Providers import.

---------

Co-authored-by: Hiroshi Horii <[email protected]>

README.md

@@ -47,8 +47,8 @@ $ python
 
 ```python
 import qiskit
-from qiskit import IBMQ
 from qiskit_aer import AerSimulator
+from qiskit.providers.fake_provider import FakeManilaV2
 
 # Generate 3-qubit GHZ state
 circ = qiskit.QuantumCircuit(3)
@@ -61,24 +61,23 @@ circ.measure_all()
 aersim = AerSimulator()
 
 # Perform an ideal simulation
-result_ideal = qiskit.execute(circ, aersim).result()
+result_ideal = aersim.run(circ).result()
 counts_ideal = result_ideal.get_counts(0)
 print('Counts(ideal):', counts_ideal)
 # Counts(ideal): {'000': 493, '111': 531}
 
 # Construct a noisy simulator backend from an IBMQ backend
 # This simulator backend will be automatically configured
-# using the device configuration and noise model 
-provider = IBMQ.load_account()
-backend = provider.get_backend('ibmq_athens')
+# using the device configuration and noise model
+backend = FakeManilaV2()
 aersim_backend = AerSimulator.from_backend(backend)
 
 # Perform noisy simulation
-result_noise = qiskit.execute(circ, aersim_backend).result()
+result_noise = aersim_backend.run(circ).result()
 counts_noise = result_noise.get_counts(0)
 
 print('Counts(noise):', counts_noise)
-# Counts(noise): {'000': 492, '001': 6, '010': 8, '011': 14, '100': 3, '101': 14, '110': 18, '111': 469}
+# Counts(noise): {'101': 16, '110': 48, '100': 7, '001': 31, '010': 7, '000': 464, '011': 15, '111': 436}
 ```
 
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