matrices.pauli
==============

.. py:module:: matrices.pauli

.. autoapi-nested-parse::

   Generates the Pauli matrices.



Functions
---------

.. autoapisummary::

   matrices.pauli.pauli


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

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

   Produce a Pauli operator :cite:`WikiPauli`.

   Produces the 2-by-2 Pauli matrix indicated by the value of :code:`ind` or a tensor product
   of Pauli matrices when :code:`ind` is provided as a list. In general, when :code:`ind` is a list
   :math:`[i_1, i_2, \dots, i_n]`, the function returns the tensor product

   .. math:: P_{i_1} \otimes P_{i_2} \otimes \cdots \otimes P_{i_n}

   where each :math:`i_k \in \{0,1,2,3\}`, with the correspondence:
   :math:`P_{0} = I`, :math:`P_{1} = X`, :math:`P_{2} = Y`, and :math:`P_{3} = Z`.

   The 2-by-2 Pauli matrices are defined as follows:

   .. 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.

   .. jupyter-execute::

    from toqito.matrices import pauli

    pauli("I")

   Example for Pauli-X matrix.

   .. jupyter-execute::

    from toqito.matrices import pauli

    pauli("X")

   Example for Pauli-Y matrix.

   .. jupyter-execute::

    from toqito.matrices import pauli

    pauli("Y")


   Example for Pauli-Z matrix.

   .. jupyter-execute::

    from toqito.matrices import pauli

    pauli("Z")

   Example using :code:`ind` as list.

   .. jupyter-execute::

    from toqito.matrices import pauli

    pauli([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.