toqito.matrices.hadamard
========================

.. py:module:: toqito.matrices.hadamard

.. autoapi-nested-parse::

   Generates a Hadamard matrix.





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

.. py:function:: hadamard(n_param = 1)

   Produce a `2^{n_param}` dimensional Hadamard matrix [@WikiHadamard].

   The standard Hadamard matrix that is often used in quantum information as a
   one-qubit quantum gate is defined as

   \[
       H_1 = \frac{1}{\sqrt{2}} \begin{pmatrix}
                                   1 & 1 \\
                                   1 & -1
                                \end{pmatrix}
   \]

   In general, the Hadamard matrix of dimension `2^{n_param}` may be
   defined as

   \[
       \left( H_n \right)_{i, j} = \frac{1}{2^{\frac{n}{2}}}
       \left(-1\right)^{i \cdot j}
   \]

   .. rubric:: Examples

   The standard 1-qubit Hadamard matrix can be generated in `toqito` as

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

   print(hadamard(1))
   ```