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

.. py:module:: toqito.matrices.pauli

.. autoapi-nested-parse::

   Generates the Pauli matrices.





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

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

   Produce a Pauli operator [@WikiPauli].

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

   \[
       P_{i_1} \otimes P_{i_2} \otimes \cdots \otimes P_{i_n}
   \]

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

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

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

   .. rubric:: Examples

   Example for identity Pauli matrix.

   ```python exec="1" source="above"
   from toqito.matrices import pauli

   print(pauli("I"))
   ```

   Example for Pauli-X matrix.

   ```python exec="1" source="above"
   from toqito.matrices import pauli

   print(pauli("X"))
   ```


   Example for Pauli-Y matrix.

   ```python exec="1" source="above"
   from toqito.matrices import pauli

   print(pauli("Y"))
   ```


   Example for Pauli-Z matrix.

   ```python exec="1" source="above"
   from toqito.matrices import pauli

   print(pauli("Z"))
   ```

   Example using `ind` as list.

   ```python exec="1" source="above"
   from toqito.matrices import pauli

   print(pauli([0,1]))
   ```

   :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
   :param False.: