:py:mod:`matrices.pauli`
========================

.. py:module:: matrices.pauli

.. autoapi-nested-parse::

   Pauli matrices.



Module Contents
---------------


Functions
~~~~~~~~~

.. autoapisummary::

   matrices.pauli.pauli



.. py:function:: pauli(ind, is_sparse = False)

   Produce a Pauli operator :cite:`WikiPauli`.

   Provides the 2-by-2 Pauli matrix indicated by the value of :code:`ind`. The
   variable :code:`ind = 1` gives the Pauli-X operator, :code:`ind = 2` gives
   the Pauli-Y operator, :code:`ind = 3` gives the Pauli-Z operator, and
   :code:`ind = 0` gives the identity operator. Alternatively, :code:`ind` can
   be set to "I", "X", "Y", or "Z" (case insensitive) to indicate the Pauli
   identity, X, Y, or Z operator.

   The 2-by-2 Pauli matrices are defined as the following matrices:

   .. math::

       \begin{equation}
           \begin{aligned}
               X = \begin{pmatrix}
                       0 & 1 \\
                       1 & 0
                   \end{pmatrix}, \quad
               Y = \begin{pmatrix}
                       0 & -i \\
                       i & 0
                   \end{pmatrix}, \quad
               Z = \begin{pmatrix}
                       1 & 0 \\
                       0 & -1
                   \end{pmatrix}, \quad
               I = \begin{pmatrix}
                       1 & 0 \\
                       0 & 1
                   \end{pmatrix}.
               \end{aligned}
           \end{equation}

   .. rubric:: Examples

   Example for identity Pauli matrix.

   >>> from toqito.matrices import pauli
   >>> pauli("I")
   array([[1., 0.],
          [0., 1.]])

   Example for Pauli-X matrix.

   >>> from toqito.matrices import pauli
   >>> pauli("X")
   array([[0, 1],
          [1, 0]])

   Example for Pauli-Y matrix.

   >>> from toqito.matrices import pauli
   >>> pauli("Y")
   array([[ 0.+0.j, -0.-1.j],
          [ 0.+1.j,  0.+0.j]])

   Example for Pauli-Z matrix.

   >>> from toqito.matrices import pauli
   >>> pauli("Z")
   array([[ 1,  0],
          [ 0, -1]])

   .. rubric:: References

   .. bibliography::
       :filter: docname in docnames

   :param ind: The index to indicate which Pauli operator to generate.
   :param is_sparse: Returns a compressed sparse row array if set to True and a non compressed
                     sparse row array if set to False.