After Aer .14 is released, remove approximation=true from relevant pa…

…ges (Qiskit#1020)

Closes Qiskit#319

---------

Co-authored-by: Frank Harkins <frankharkins@hotmail.co.uk>

docs/api/migration-guides/qiskit-algorithms-module.mdx

@@ -145,13 +145,13 @@ This guide describes these common configurations for algorithms that determine w
 * Running an algorithm on an Aer simulator using a custom instruction.  For example, using the [`qiskit.opflow`](../qiskit/0.46/opflow) legacy
 [`qiskit.opflow.expectations.AerPauliExpectation`](../qiskit/0.46/qiskit.opflow.expectations.AerPauliExpectation).
 
-- Aer Primitives with `shots=None`, `approximation=True`.  See [TrotterQRTE](#trotterqrte) for examples.
+- Aer Primitives with default options.  See [TrotterQRTE](#trotterqrte) for examples.
 
 ```python
 from qiskit_aer.primitives import Sampler, Estimator
 
-sampler = Sampler(run_options={"approximation": True, "shots": None})
-estimator = Estimator(run_options={"approximation": True, "shots": None})
+sampler = Sampler()
+estimator = Estimator()
 ```
 
 <span id="eigen"></span>
@@ -706,7 +706,7 @@ time = 1
 evolution_problem = TimeEvolutionProblem(operator, 1, initial_state)
 
 # Aer simulator using custom instruction
-estimator = AerEstimator(run_options={"approximation": True, "shots": None})
+estimator = AerEstimator()
 
 # LieTrotter with 1 rep
 trotter_qrte = TrotterQRTE(estimator=estimator)

docs/api/migration-guides/qiskit-opflow-module.mdx

@@ -950,7 +950,7 @@ are different `Estimator` implementations, as noted [previously.](#attention_pri
 | Opflow | Alternative |
 | --- | --- |
 | [`qiskit.opflow.expectations.ExpectationFactory`](../qiskit/0.46/qiskit.opflow.expectations.ExpectationFactory) | No direct replacement. This class was used to create instances of one of the classes listed below. |
-| [`qiskit.opflow.expectations.AerPauliExpectation`](../qiskit/0.46/qiskit.opflow.expectations.AerPauliExpectation) | Use [`qiskit_aer.primitives.Estimator`](https://qiskit.org/ecosystem/aer/stubs/qiskit_aer.primitives.Estimator.html)  with `approximation=True`, and then `shots=None` as `run_options`. See example below. |
+| [`qiskit.opflow.expectations.AerPauliExpectation`](../qiskit/0.46/qiskit.opflow.expectations.AerPauliExpectation) | Use [`qiskit_aer.primitives.Estimator`](https://qiskit.org/ecosystem/aer/stubs/qiskit_aer.primitives.Estimator.html). See example below. |
 | [`qiskit.opflow.expectations.MatrixExpectation`](../qiskit/0.46/qiskit.opflow.expectations.MatrixExpectation) | Use [`qiskit.primitives.Estimator`](../qiskit/qiskit.primitives.Estimator) primitive. If no shots are set, it performs an exact Statevector calculation. See example below. |
 | [`qiskit.opflow.expectations.PauliExpectation`](../qiskit/0.46/qiskit.opflow.expectations.PauliExpectation) | Use any Estimator primitive. For [`qiskit.primitives.Estimator`](../qiskit/qiskit.primitives.Estimator), set `shots!=None` for a shotbased simulation. For [`qiskit_aer.primitives.Estimator`](https://qiskit.org/ecosystem/aer/stubs/qiskit_aer.primitives.Estimator.html), this is the default. |
 
@@ -989,7 +989,7 @@ from qiskit.quantum_info import SparsePauliOp
 from qiskit import QuantumCircuit
 from qiskit_aer.primitives import Estimator
 
-estimator = Estimator(approximation=True, run_options={"shots": None})
+estimator = Estimator()
 
 op = SparsePauliOp.from_list([("X", 1j)])
 states_op = QuantumCircuit(1)

docs/verify/simulate-with-qiskit-aer.ipynb

@@ -49,11 +49,7 @@
    "id": "db010004-7a23-4c64-9cb3-8768f805e22a",
    "metadata": {},
    "source": [
-    "This circuit contains parameters to represent the rotation angles for $R_y$ and $R_z$ gates. When simulating this circuit, we need to specify explicit values for these parameters. In the next cell, we specify some values for these parameters and use the [Estimator](https://qiskit.org/ecosystem/aer/stubs/qiskit_aer.primitives.Estimator.html) primitive from Qiskit Aer to compute the exact expectation value of the observable $ZZ \\cdots Z$.\n",
-    "\n",
-    "<Admonition type=\"note\">\n",
-    "Setting `approximation=True` when initializing the Estimator tells Qiskit Aer to approximate the effect of sampling error rather than actually perform sampling. This makes the simulation much more efficient, and also allows us to calculate the exact expectation value, free of sampling error. After Qiskit Aer 0.14, this will be the default behavior, so we won't need to specify this argument.\n",
-    "</Admonition>"
+    "This circuit contains parameters to represent the rotation angles for $R_y$ and $R_z$ gates. When simulating this circuit, we need to specify explicit values for these parameters. In the next cell, we specify some values for these parameters and use the [Estimator](https://qiskit.org/ecosystem/aer/stubs/qiskit_aer.primitives.Estimator.html) primitive from Qiskit Aer to compute the exact expectation value of the observable $ZZ \\cdots Z$."
    ]
   },
   {
@@ -80,7 +76,7 @@
     "observable = SparsePauliOp(\"Z\" * n_qubits)\n",
     "params = [0.1] * circuit.num_parameters\n",
     "\n",
-    "exact_estimator = Estimator(approximation=True)\n",
+    "exact_estimator = Estimator()\n",
     "job = exact_estimator.run(circuit, observable, params)\n",
     "exact_value = job.result().values[0]\n",
     "exact_value"
@@ -123,7 +119,7 @@
     ")\n",
     "\n",
     "noisy_estimator = Estimator(\n",
-    "    backend_options={\"noise_model\": noise_model}, approximation=True\n",
+    "    backend_options={\"noise_model\": noise_model}\n",
     ")\n",
     "job = noisy_estimator.run(circuit, observable, params)\n",
     "noisy_value = job.result().values[0]\n",

docs/verify/stabilizer-circuit-simulation.ipynb

@@ -181,7 +181,6 @@
     "\n",
     "exact_estimator = Estimator(\n",
     "    backend_options=dict(method=\"stabilizer\"),\n",
-    "    approximation=True,\n",
     ")\n",
     "job = exact_estimator.run(circuit, observable, params)\n",
     "exact_value = job.result().values[0]\n",