Update introduction to Qiskit (Qiskit/qiskit-metapackage#1669)

* Update introduction to Qiskit

* update docs

---------

Co-authored-by: Luciano Bello <bel@zurich.ibm.com>
Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>

docs/intro_tutorial1.rst

@@ -19,13 +19,12 @@ subsequent sections:
 
 .. jupyter-execute::
 
-    import numpy as np
     from qiskit import QuantumCircuit, transpile
-    from qiskit.providers.aer import QasmSimulator
+    from qiskit_aer import AerSimulator
     from qiskit.visualization import plot_histogram
 
-    # Use Aer's qasm_simulator
-    simulator = QasmSimulator()
+    # Use Aer's AerSimulator
+    simulator = AerSimulator()
 
     # Create a Quantum Circuit acting on the q register
     circuit = QuantumCircuit(2, 2)
@@ -37,21 +36,21 @@ subsequent sections:
     circuit.cx(0, 1)
 
     # Map the quantum measurement to the classical bits
-    circuit.measure([0,1], [0,1])
+    circuit.measure([0, 1], [0, 1])
 
-    # compile the circuit down to low-level QASM instructions
-    # supported by the backend (not needed for simple circuits)
+    # Compile the circuit for the support instruction set (basis_gates)
+    # and topology (coupling_map) of the backend
     compiled_circuit = transpile(circuit, simulator)
 
-    # Execute the circuit on the qasm simulator
+    # Execute the circuit on the aer simulator
     job = simulator.run(compiled_circuit, shots=1000)
 
     # Grab results from the job
     result = job.result()
 
     # Returns counts
     counts = result.get_counts(compiled_circuit)
-    print("\nTotal count for 00 and 11 are:",counts)
+    print("\nTotal count for 00 and 11 are:", counts)
 
     # Draw the circuit
     circuit.draw()
@@ -85,16 +84,15 @@ The basic elements needed for your program are imported as follows:
 
 .. code-block:: python
 
-  import numpy as np
   from qiskit import QuantumCircuit
-  from qiskit.providers.aer import QasmSimulator
+  from qiskit_aer import AerSimulator
   from qiskit.visualization import plot_histogram
 
 In more detail, the imports are
 
 - ``QuantumCircuit``: can be thought as the instructions of the quantum system.
   It holds all your quantum operations.
-- ``QasmSimulator``: is the Aer high performance circuit simulator.
+- ``AerSimulator``: is the Aer high performance circuit simulator.
 - ``plot_histogram``: creates histograms.
 
 
@@ -130,7 +128,7 @@ Consider the following three lines of code:
 
     circuit.h(0)
     circuit.cx(0, 1)
-    circuit.measure([0,1], [0,1])
+    circuit.measure([0, 1], [0, 1])
 
 The gates are added to the circuit one-by-one to form the Bell state
 
@@ -194,19 +192,18 @@ If you have issues installing Aer, you can alternatively use the Basic Aer
 provider by replacing `Aer` with `BasicAer`. Basic Aer is included in Qiskit
 Terra.
 
-.. code-block:: text
+.. code-block:: python
 
-    import numpy as np
     from qiskit import QuantumCircuit, transpile
     from qiskit.providers.basicaer import QasmSimulatorPy
     ...
 
-To simulate this circuit, you will use the ``qasm_simulator``. Each run of this
+To simulate this circuit, you will use the ``AerSimulator``. Each run of this
 circuit will yield either the bit string 00 or 11.
 
 .. jupyter-execute::
 
-    simulator = QasmSimulator()
+    simulator = AerSimulator()
     compiled_circuit = transpile(circuit, simulator)
     job = simulator.run(compiled_circuit, shots=1000)
     result = job.result()