toqito.matrices.gen_pauli¶
Produces the generalized Pauli operator matrices.
Module Contents¶
- toqito.matrices.gen_pauli.gen_pauli(k_1, k_2, dim)[source]¶
Produce generalized Pauli operator [@WikiPauliGen].
Generates a dim-by-dim unitary operator. More specifically, it is the operator (X^k_1 Z^k_2), where (X) and (Z) are the “gen_pauli_x” and “gen_pauli_z” operators that naturally generalize the Pauli X and Z operators. These matrices span the entire space of dim-by-dim matrices as k_1 and k_2 range from 0 to dim-1, inclusive.
Note that the generalized Pauli operators are also known by the name of “discrete Weyl operators”. (Lecture 6: Further Remarks On Measurements And Channels from [@Watrous_2011_Lecture_Notes])
Examples
The generalized Pauli operator for k_1 = 1, k_2 = 0, and dim = 2 is given as the standard Pauli-X matrix
- [
- G_{1, 0, 2} = begin{pmatrix}
0 & 1 \ 1 & 0
end{pmatrix}.
]
This can be obtained in |toqito⟩ as follows.
```python exec=”1” source=”above” from toqito.matrices import gen_pauli
print(gen_pauli(k_1=1, k_2=0, dim=2)) ```
The generalized Pauli matrix k_1 = 1, k_2 = 1, and dim = 2 is given as the standard Pauli-Y matrix
- [
- G_{1, 1, 2} = begin{pmatrix}
0 & -1 \ 1 & 0
end{pmatrix}.
]
This can be obtained in |toqito⟩ as follows.
```python exec=”1” source=”above” from toqito.matrices import gen_pauli
print(gen_pauli(k_1=1, k_2=1, dim=2)) ```
- Parameters:
k_1 (int) – (a non-negative integer from 0 to dim-1 inclusive).
k_2 (int) – (a non-negative integer from 0 to dim-1 inclusive).
dim (int) – (a positive integer indicating the dimension).
- Returns:
A generalized Pauli operator.
- Return type:
numpy.ndarray