toqito.matrices.gen_pauli_z¶
Produces a generalized Pauli-Z operator matrix.
Module Contents¶
- toqito.matrices.gen_pauli_z.gen_pauli_z(dim)[source]¶
Produce gen_pauli_z matrix [@WikiClock].
Returns the gen_pauli_z matrix of dimension dim described in [@WikiClock]. The gen_pauli_z matrix generates the following dim-by-dim matrix
- [
- Sigma_{1, d} = begin{pmatrix}
1 & 0 & 0 & ldots & 0 \ 0 & omega & 0 & ldots & 0 \ 0 & 0 & omega^2 & ldots & 0 \ vdots & vdots & vdots & ddots & vdots \ 0 & 0 & 0 & ldots & omega^{d-1}
end{pmatrix}
]
where (omega) is the n-th primitive root of unity.
The gen_pauli_z matrix is primarily used in the construction of the generalized Pauli operators.
Examples
The gen_pauli_z matrix generated from (d = 3) yields the following matrix:
- [
- Sigma_{1, 3} = begin{pmatrix}
1 & 0 & 0 \ 0 & omega & 0 \ 0 & 0 & omega^2
end{pmatrix}
]
```python exec=”1” source=”above” from toqito.matrices import gen_pauli_z
- Parameters:
dim (int) – Dimension of the matrix.
- Returns:
dim-by-dim gen_pauli_z matrix.
- Return type:
numpy.ndarray