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+#########################
+Order of qubits in Qiskit
+#########################
+
+While most physics textbooks represent an :math:`n`-qubit system as the tensor product :math:`Q_0\otimes Q_1 \otimes ... \otimes Q_{n-1}`, where :math:`Q_j` is the :math:`j^{\mathrm{th}}` qubit, Qiskit uses the inverse order, that is, :math:`Q_{n-1}\otimes ... \otimes Q_1 \otimes Q_{0}`. As explained in `this video <https://www.youtube.com/watch?v=EiqHj3_Avps>`_ from `Qiskit's YouTube channel <https://www.youtube.com/@qiskit>`_, this is done to follow the convention in classical computing, in which the :math:`n^{\mathrm{th}}` bit or most significant bit (MSB) is placed on the left (with index 0) while the least significant bit (LSB) is placed on the right (index :math:`n-1`). This ordering convention is called little-endian while the one from the physics textbooks is called big-endian.
+
+This means that if we have, for example, a 3-qubit system with qubit 0 in state :math:`|1\rangle` and qubits 1 and 2 in state :math:`|0\rangle`, Qiskit would represent this state as :math:`|001\rangle` while most physics textbooks would represent this state as :math:`|100\rangle`. 
+
+The matrix representation of any multi-qubit gate is also affected by this different qubit ordering. For example, if we consider the single-qubit gate
+
+.. math::
+
+    U = \begin{pmatrix} u_{00} & u_{01} \\ u_{10} & u_{11} \end{pmatrix}
+
+And we want a controlled version :math:`C_U` whose control qubit is qubit 0 and whose target is qubit 1, following Qiskit's ordering its matrix representation would be
+
+.. math::
+
+    C_U = \begin{pmatrix} 1 & 0 & 0 & 0 \\0 & u_{00} & 0 & u_{01} \\ 0 & 0 & 1 & 0 \\ 0 & u_{10} & 0& u_{11} \end{pmatrix}
+
+while in a physics textbook it would be written as 
+
+.. math::
+
+    C_U = \begin{pmatrix} 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\ 0 & 0 & u_{00} & u_{01} \\ 0 & 0 & u_{00} & u_{01} \end{pmatrix}
+
+
+For more details about how this ordering of MSB and LSB affects the matrix representation of any particular gate, check its entry in the circuit :mod:`~qiskit.circuit.library`.
+
+This different order can also make the circuit corresponding to an algorithm from a textbook a bit more complicated to visualize. Fortunately, Qiskit provides a way to represent a :class:`~.QuantumCircuit` with the most significant qubits on top, just like in the textbooks. This can be done by setting the ``reverse_bits`` argument of the :meth:`~.QuantumCircuit.draw` method to ``True``.
+
+Let's try this for a 3-qubit Quantum Fourier Transform (:class:`~.QFT`).
+
+.. plot::
+    :include-source:
+    :context:
+
+    from qiskit.circuit.library import QFT
+
+    qft = QFT(3)
+    qft.decompose().draw('mpl')
+
+.. plot::
+    :include-source:
+    :context: close-figs
+
+    qft.decompose().draw('mpl', reverse_bits=True)
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+.. _faq:
+
+==========================
+Frequently Asked Questions
+==========================
+
+**Q: How should I cite Qiskit in my research?**
+
+**A:** Please cite Qiskit by using the included `BibTeX file
+<https://github.com/Qiskit/qiskit-terra/blob/main/CITATION.bib>`__.
+
+|
+
+**Q: Why do I receive the error message** ``AttributeError: QuantumCircuit object has no attribute save_state``
+**when using ``save_*``method on a circuit?**
+
+**A:** The ``save_*`` instructions are part of Qiskit Aer project,
+a high performance simulator for quantum circuits. These instructions do not
+exist outside of Qiskit Aer and are added dynamically to the
+:class:`~.QuantumCircuit` class by Qiskit Aer on import. If you would like to
+use these instructions you must first ensure that you have imported
+``qiskit_aer`` in your program before trying to call these methods. You
+can refer to :mod:`qiskit_aer.library` for the details of these custom
+instructions included with Qiskit Aer.
+
+**Q: Why do my results from real devices differ from my results from the simulator?**
+
+**A:** The simulator runs jobs as though is was in an ideal environment; one
+without noise or decoherence. However, when jobs are run on the real devices
+there is noise from the environment and decoherence, which causes the qubits
+to behave differently than what is intended.
+
+|
+
+**Q: Why do I receive the error message,** ``No Module 'qiskit'`` **when using Jupyter Notebook?**
+
+**A:** If you used ``pip install qiskit`` and set up your virtual environment in
+Anaconda, then you may experience this error when you run a tutorial
+in Jupyter Notebook. If you have not installed Qiskit or set up your
+virtual environment, you can follow the :ref:`installation` steps.
+
+The error is caused when trying to import the Qiskit package in an
+environment where Qiskit is not installed. If you launched Jupyter Notebook
+from the Anaconda-Navigator, it is possible that Jupyter Notebook is running
+in the base (root) environment, instead of in your virtual
+environment. Choose a virtual environment in the Anaconda-Navigator from the
+**Applications on** dropdown menu. In this menu, you can see
+all of the virtual environments within Anaconda, and you can
+select the environment where you have Qiskit installed to launch Jupyter
+Notebook.
+
+|
+
+**Q: Why am I getting a compilation error while installing ``qiskit``?**
+
+**A:** Qiskit depends on a number of other open source Python packages, which
+are automatically installed when doing ``pip install qiskit``. Depending on
+your system's platform and Python version, it is possible that a particular
+package does not provide pre-built binaries for your system. You can refer
+to :ref:`platform_support` for a list of platforms supported by Qiskit, some
+of which may need an extra compiler. In cases where there are
+no precompiled binaries available ``pip`` will attempt to compile the package
+from source, which in turn might require some extra dependencies that need to
+be installed manually.
+
+If the output of ``pip install qiskit`` contains similar lines to:
+
+.. code:: sh
+
+  Failed building wheel for SOME_PACKAGE
+  ...
+  build/temp.linux-x86_64-3.5/_openssl.c:498:30: fatal error
+  compilation terminated.
+  error: command 'x86_64-linux-gnu-gcc' failed with exit status 1
+
+please check the documentation of the package that failed to install (in the
+example code, ``SOME_PACKAGE``) for information on how to install the libraries
+needed for compiling from source.
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+###############################################################
+Compute circuit output probabilities with ``Sampler`` primitive
+###############################################################
+
+This guide shows how to get the probability distribution of a quantum circuit with the :class:`~qiskit.primitives.Sampler` primitive.
+
+.. note::
+
+    While this guide uses Qiskit’s reference implementation, the ``Sampler`` primitive can be run with any provider using :class:`~qiskit.primitives.BackendSampler`.
+    
+    .. code-block::
+
+        from qiskit.primitives import BackendSampler
+        from <some_qiskit_provider> import QiskitProvider
+
+        provider = QiskitProvider()
+        backend = provider.get_backend('backend_name')
+        sampler = BackendSampler(backend)
+
+    There are some providers that implement primitives natively (see `this page <http://qiskit.org/providers/#primitives>`_ for more details).
+
+Initialize quantum circuits
+===========================
+
+The first step is to create the :class:`~qiskit.circuit.QuantumCircuit`\ s from which you want to obtain the probability distribution.
+
+.. plot::
+    :include-source:
+
+    from qiskit import QuantumCircuit
+
+    qc = QuantumCircuit(2)
+    qc.h(0)
+    qc.cx(0,1)
+    qc.measure_all()
+    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)
+    qc.measure_all()
+
+.. note::
+
+    The :class:`~qiskit.circuit.QuantumCircuit` you pass to :class:`~qiskit.primitives.Sampler` has to include measurements.
+
+Initialize the ``Sampler``
+==========================
+
+Then, you need to create a :class:`~qiskit.primitives.Sampler` instance.
+
+.. testcode::
+
+    from qiskit.primitives import Sampler
+
+    sampler = Sampler()
+
+Run and get results
+===================
+
+Now that you have defined your ``sampler``, you can run it by calling the :meth:`~qiskit.primitives.Sampler.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.SamplerResult` object) 
+with the :meth:`~qiskit.providers.JobV1.result` method.
+
+.. testcode::
+
+    job = sampler.run(qc)
+    result = job.result()
+    print(result)
+
+.. testoutput::
+
+    SamplerResult(quasi_dists=[{0: 0.4999999999999999, 3: 0.4999999999999999}], metadata=[{}])
+
+While this example only uses one :class:`~qiskit.circuit.QuantumCircuit`, if you want to sample multiple circuits you can
+pass a ``list`` of :class:`~qiskit.circuit.QuantumCircuit` instances to the :meth:`~qiskit.primitives.Sampler.run` method.
+
+Get the probability distribution
+--------------------------------
+
+From these results you can extract the quasi-probability distributions with the attribute :attr:`~qiskit.primitives.SamplerResult.quasi_dists`.
+
+Even though there is only one circuit in this example, :attr:`~qiskit.primitives.SamplerResult.quasi_dists` returns a list of :class:`~qiskit.result.QuasiDistribution`\ s.
+``result.quasi_dists[i]`` is the quasi-probability distribution of the ``i``-th circuit.
+
+.. note::
+
+    A quasi-probability distribution differs from a probability distribution in that negative values are also allowed.
+    However the quasi-probabilities must sum up to 1 like probabilities.
+    Negative quasi-probabilities may appear when using error mitigation techniques.
+
+.. testcode::
+
+    quasi_dist = result.quasi_dists[0]
+    print(quasi_dist)
+
+.. testoutput::
+
+    {0: 0.4999999999999999, 3: 0.4999999999999999}
+
+Probability distribution with binary outputs
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+If you prefer to see the output keys as binary strings instead of decimal numbers, you can use the
+:meth:`~qiskit.result.QuasiDistribution.binary_probabilities` method.
+
+.. testcode::
+    
+    print(quasi_dist.binary_probabilities())
+
+.. testoutput::
+
+    {'00': 0.4999999999999999, '11': 0.4999999999999999}
+
+Parameterized circuit with ``Sampler``
+========================================
+
+The :class:`~qiskit.primitives.Sampler` 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)
+    param_qc.measure_all()
+    print(param_qc.draw())
+
+.. testoutput::
+
+            ┌───────┐      ░ ┌─┐   
+       q_0: ┤ Ry(θ) ├──■───░─┤M├───
+            └───────┘┌─┴─┐ ░ └╥┘┌─┐
+       q_1: ─────────┤ X ├─░──╫─┤M├
+                     └───┘ ░  ║ └╥┘
+    meas: 2/══════════════════╩══╩═
+                              0  1 
+
+The main difference from 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.
+
+.. testcode::
+
+    import numpy as np
+
+    parameter_values = [[0], [np.pi/6], [np.pi/2]]
+
+    job = sampler.run([param_qc]*3, parameter_values=parameter_values)
+    dists = job.result().quasi_dists
+
+    for i in range(3):
+        print(f"Parameter: {parameter_values[i][0]:.5f}\t Probabilities: {dists[i]}")
+
+.. testoutput::
+
+    Parameter: 0.00000	 Probabilities: {0: 1.0}
+    Parameter: 0.52360	 Probabilities: {0: 0.9330127018922194, 3: 0.0669872981077807}
+    Parameter: 1.57080	 Probabilities: {0: 0.5000000000000001, 3: 0.4999999999999999}
+
+Change run options
+==================
+
+Your workflow might require tuning primitive run options, such as the amount of shots.
+
+By default, the reference :class:`~qiskit.primitives.Sampler` 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.Sampler`:
+
+* Set keyword arguments in the :meth:`~qiskit.primitives.Sampler.run` method.
+* Modify :class:`~qiskit.primitives.Sampler` options.
+
+Set keyword arguments for :meth:`~qiskit.primitives.Sampler.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.Sampler.run` method. You can do this by
+passing them as keyword arguments.
+
+.. testcode::
+
+    job = sampler.run(qc, shots=2048, seed=123)
+    result = job.result()
+    print(result)
+
+.. testoutput::
+
+    SamplerResult(quasi_dists=[{0: 0.5205078125, 3: 0.4794921875}], metadata=[{'shots': 2048}])
+
+Modify :class:`~qiskit.primitives.Sampler` options
+---------------------------------------------------
+
+If you want to keep some configuration values for several runs, it can be better to
+change the :class:`~qiskit.primitives.Sampler` options. That way you can use the same 
+:class:`~qiskit.primitives.Sampler` object as many times as you wish without having to
+rewrite the configuration values every time you use :meth:`~qiskit.primitives.Sampler.run`.
+
+Modify existing :class:`~qiskit.primitives.Sampler`
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+If you prefer to change the options of an already-defined :class:`~qiskit.primitives.Sampler`, you can use
+:meth:`~qiskit.primitives.Sampler.set_options` and introduce the new options as keyword arguments.
+
+.. testcode::
+
+    sampler.set_options(shots=2048, seed=123)
+
+    job = sampler.run(qc)
+    result = job.result()
+    print(result)
+
+.. testoutput::
+
+    SamplerResult(quasi_dists=[{0: 0.5205078125, 3: 0.4794921875}], metadata=[{'shots': 2048}])
+
+Define a new :class:`~qiskit.primitives.Sampler` with the options
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+If you prefer to define a new :class:`~qiskit.primitives.Sampler` 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.Sampler` with the
+``options`` argument.
+
+.. testcode::
+
+    sampler = Sampler(options=options)
+
+    job = sampler.run(qc)
+    result = job.result()
+    print(result)
+
+.. testoutput::
+
+    SamplerResult(quasi_dists=[{0: 0.5205078125, 3: 0.4794921875}], metadata=[{'shots': 2048}])