toqito.matrices.hadamard

Generates a Hadamard matrix.

Module Contents

toqito.matrices.hadamard.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(-1right)^{i cdot j}

]

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)) ```

Parameters:

n_param (int)

Return type:

numpy.ndarray