matrices.pauli¶
Generates the Pauli matrices.
Functions¶
Module Contents¶
- matrices.pauli.pauli(ind, is_sparse=False)¶
Produce a Pauli operator [1].
Produces the 2-by-2 Pauli matrix indicated by the value of
indor a tensor product of Pauli matrices whenindis provided as a list. In general, whenindis 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:
\[\begin{split}\begin{equation} \begin{aligned} X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}, \quad Y = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}, \quad Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}, \quad I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}. \end{aligned} \end{equation}\end{split}\]Examples
Example for identity Pauli matrix.
>>> from toqito.matrices import pauli >>> pauli("I") array([[1., 0.], [0., 1.]])
Example for Pauli-X matrix.
>>> from toqito.matrices import pauli >>> pauli("X") array([[0, 1], [1, 0]])
Example for Pauli-Y matrix.
>>> from toqito.matrices import pauli >>> pauli("Y") array([[ 0.+0.j, -0.-1.j], [ 0.+1.j, 0.+0.j]])
Example for Pauli-Z matrix.
>>> from toqito.matrices import pauli >>> pauli("Z") array([[ 1, 0], [ 0, -1]])
Example using \(ind\) as list.
>>> from toqito.matrices import pauli >>> pauli([0,1]) array([[0., 1., 0., 0.], [1., 0., 0., 0.], [0., 0., 0., 1.], [0., 0., 1., 0.]])
References
- 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