Migrate missing estimator how to from Qiskit (Qiskit/qiskit#9716)

qiskit-docs/how_to/use_estimator.rst

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+#########################################################
+Compute an expectation value with ``Estimator`` primitive
+#########################################################
+
+This guide shows how to get the expected value of an observable for a given quantum circuit with the :class:`~qiskit.primitives.Estimator` primitive.
+
+.. note::
+
+    While this guide uses Qiskit’s reference implementation, the ``Estimator`` primitive can be run with any provider using :class:`~qiskit.primitives.BackendEstimator` .
+
+    .. code-block::
+
+        from qiskit.primitives import BackendEstimator
+        from <some_qiskit_provider> import QiskitProvider
+
+        provider = QiskitProvider()
+        backend = provider.get_backend('backend_name')
+        estimator = BackendEstimator(backend)
+
+    There are some providers that implement primitives natively (see `this page <http://qiskit.org/providers/#primitives>`_ for more details).
+
+
+Initialize observables
+======================
+
+The first step is to define the observables whose expected value you want to compute. Each observable can be any ``BaseOperator``, like the operators from :mod:`qiskit.quantum_info`.
+Among them it is preferable to use :class:`~qiskit.quantum_info.SparsePauliOp`.
+
+.. testcode::
+
+    from qiskit.quantum_info import SparsePauliOp
+
+    observable = SparsePauliOp(["II", "XX", "YY", "ZZ"], coeffs=[1, 1, -1, 1])
+
+Initialize quantum circuit
+==========================
+
+Then you need to create the :class:`~qiskit.circuit.QuantumCircuit`\ s for which you want to obtain the expected value.
+
+.. plot::
+    :include-source:
+
+    from qiskit import QuantumCircuit
+
+    qc = QuantumCircuit(2)
+    qc.h(0)
+    qc.cx(0,1)
+    qc.draw("mpl")
+
+.. testsetup::
+
+    # This code is repeated (but hidden) because we will need to use the variables with the extension sphinx.ext.doctest (testsetup/testcode/testoutput directives)
+    # and we can't reuse the variables from the plot directive above because they are incompatible.
+    # The plot directive is used to draw the circuit with matplotlib and the code is shown because of the include-source flag.
+
+    from qiskit import QuantumCircuit
+
+    qc = QuantumCircuit(2)
+    qc.h(0)
+    qc.cx(0,1)
+
+.. note::
+
+    The :class:`~qiskit.circuit.QuantumCircuit` you pass to :class:`~qiskit.primitives.Estimator` must not include any measurements.
+
+Initialize the ``Estimator``
+============================
+
+Then, you need to instantiate an :class:`~qiskit.primitives.Estimator`.
+
+.. testcode::
+
+    from qiskit.primitives import Estimator
+
+    estimator = Estimator()
+
+Run and get results
+===================
+
+Now that you have defined your ``estimator``, you can run your estimation by calling the :meth:`~qiskit.primitives.Estimator.run` method, 
+which returns an instance of :class:`~.PrimitiveJob` (subclass of :class:`~qiskit.providers.JobV1`). You can get the results from the job (as a :class:`~qiskit.primitives.EstimatorResult` object) 
+with the :meth:`~qiskit.providers.JobV1.result` method.
+
+.. testcode::
+
+    job = estimator.run(qc, observable)
+    result = job.result()
+    print(result)
+
+.. testoutput::
+
+    EstimatorResult(values=array([4.]), metadata=[{}])
+
+While this example only uses one :class:`~qiskit.circuit.QuantumCircuit` and one observable, if you want to get expectation values for multiple circuits and observables you can
+pass a ``list`` of :class:`~qiskit.circuit.QuantumCircuit`\ s and a list of ``BaseOperator``\ s to the :meth:`~qiskit.primitives.Estimator.run` method. Both ``list``\ s must have
+the same length.
+
+Get the expected value
+----------------------
+
+From these results you can extract the expected values with the attribute :attr:`~qiskit.primitives.EstimatorResult.values`.
+
+:attr:`~qiskit.primitives.EstimatorResult.values` returns a :class:`numpy.ndarray`
+whose ``i``-th element is the expectation value corresponding to the ``i``-th circuit and ``i``-th observable.
+
+.. testcode::
+
+    exp_value = result.values[0]
+    print(exp_value)
+
+.. testoutput::
+
+    3.999999999999999
+
+Parameterized circuit with ``Estimator``
+========================================
+
+The :class:`~qiskit.primitives.Estimator` primitive can be run with unbound parameterized circuits like the one below.
+You can also manually bind values to the parameters of the circuit and follow the steps
+of the previous example.
+
+.. testcode::
+
+    from qiskit.circuit import Parameter
+
+    theta = Parameter('θ')
+    param_qc = QuantumCircuit(2)
+    param_qc.ry(theta, 0)
+    param_qc.cx(0,1)
+    print(param_qc.draw())
+
+.. testoutput::
+
+         ┌───────┐     
+    q_0: ┤ Ry(θ) ├──■──
+         └───────┘┌─┴─┐
+    q_1: ─────────┤ X ├
+                  └───┘
+
+The main difference with the previous case is that now you need to specify the sets of parameter values
+for which you want to evaluate the expectation value as a ``list`` of ``list``\ s of ``float``\ s.
+The ``i``-th element of the outer``list`` is the set of parameter values
+that corresponds to the ``i``-th circuit and observable.
+
+.. testcode::
+
+    import numpy as np
+
+    parameter_values = [[0], [np.pi/6], [np.pi/2]]
+
+    job = estimator.run([param_qc]*3, [observable]*3, parameter_values=parameter_values)
+    values = job.result().values
+
+    for i in range(3):
+        print(f"Parameter: {parameter_values[i][0]:.5f}\t Expectation value: {values[i]}")
+
+.. testoutput::
+
+    Parameter: 0.00000	 Expectation value: 2.0
+    Parameter: 0.52360	 Expectation value: 3.0
+    Parameter: 1.57080	 Expectation value: 4.0
+
+Change run options
+==================
+
+Your workflow might require tuning primitive run options, such as the amount of shots.
+
+By default, the reference :class:`~qiskit.primitives.Estimator` class performs an exact statevector
+calculation based on the :class:`~qiskit.quantum_info.Statevector` class. However, this can be 
+modified to include shot noise if the number of ``shots`` is set. 
+For reproducibility purposes, a ``seed`` will also be set in the following examples.
+
+There are two main ways of setting options in the :class:`~qiskit.primitives.Estimator`:
+
+* Set keyword arguments in the :meth:`~qiskit.primitives.Estimator.run` method.
+* Modify :class:`~qiskit.primitives.Estimator` options.
+
+Set keyword arguments for :meth:`~qiskit.primitives.Estimator.run`
+------------------------------------------------------------------
+
+If you only want to change the settings for a specific run, it can be more convenient to
+set the options inside the :meth:`~qiskit.primitives.Estimator.run` method. You can do this by
+passing them as keyword arguments.
+
+.. testcode::
+
+    job = estimator.run(qc, observable, shots=2048, seed=123)
+    result = job.result()
+    print(result)
+
+.. testoutput::
+
+    EstimatorResult(values=array([4.]), metadata=[{'variance': 3.552713678800501e-15, 'shots': 2048}])
+
+.. testcode::
+
+    print(result.values[0])
+
+.. testoutput::
+
+    3.999999998697238
+
+Modify :class:`~qiskit.primitives.Estimator` options
+-----------------------------------------------------
+
+If you want to keep some configuration values for several runs, it can be better to
+change the :class:`~qiskit.primitives.Estimator` options. That way you can use the same 
+:class:`~qiskit.primitives.Estimator` object as many times as you wish without having to
+rewrite the configuration values every time you use :meth:`~qiskit.primitives.Estimator.run`.
+
+Modify existing :class:`~qiskit.primitives.Estimator`
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+If you prefer to change the options of an already-defined :class:`~qiskit.primitives.Estimator`, you can use
+:meth:`~qiskit.primitives.Estimator.set_options` and introduce the new options as keyword arguments.
+
+.. testcode::
+
+    estimator.set_options(shots=2048, seed=123)
+
+    job = estimator.run(qc, observable)
+    result = job.result()
+    print(result)
+
+.. testoutput::
+
+    EstimatorResult(values=array([4.]), metadata=[{'variance': 3.552713678800501e-15, 'shots': 2048}])
+
+.. testcode::
+
+    print(result.values[0])
+
+.. testoutput::
+
+    3.999999998697238
+
+
+Define a new :class:`~qiskit.primitives.Estimator` with the options
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+If you prefer to define a new :class:`~qiskit.primitives.Estimator` with new options, you need to
+define a ``dict`` like this one:
+
+.. testcode::
+
+    options = {"shots": 2048, "seed": 123}
+
+And then you can introduce it into your new :class:`~qiskit.primitives.Estimator` with the
+``options`` argument.
+
+.. testcode::
+
+    estimator = Estimator(options=options)
+
+    job = estimator.run(qc, observable)
+    result = job.result()
+    print(result)
+
+.. testoutput::
+
+    EstimatorResult(values=array([4.]), metadata=[{'variance': 3.552713678800501e-15, 'shots': 2048}])
+
+.. testcode::
+
+    print(result.values[0])
+
+.. testoutput::
+
+    3.999999998697238