toqito.matrices.pauli¶
Generates the Pauli matrices.
Module Contents¶
- toqito.matrices.pauli.pauli(ind, is_sparse=False)[source]¶
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}
]
Examples
Example for identity Pauli matrix.
```python exec=”1” source=”above” from toqito.matrices import pauli
Example for Pauli-X matrix.
```python exec=”1” source=”above” from toqito.matrices import pauli
Example for Pauli-Y matrix.
```python exec=”1” source=”above” from toqito.matrices import pauli
Example for Pauli-Z matrix.
```python exec=”1” source=”above” from toqito.matrices import pauli
Example using ind as list.
```python exec=”1” source=”above” from toqito.matrices import pauli
- Parameters:
ind (int | str | list[int] | list[str]) – The index to indicate which Pauli operator to generate.
is_sparse (bool) – Returns a compressed sparse row array if set to True and a non compressed sparse row array if set to
False.
- Return type:
numpy.ndarray | scipy.sparse.csr_array | None