matrices.pauli

Pauli matrices.

Module Contents

Functions

pauli(ind[, is_sparse])

Produce a Pauli operator [1].
matrices.pauli.pauli(ind, is_sparse=False)

Produce a Pauli operator [1].

Provides the 2-by-2 Pauli matrix indicated by the value of ind. The variable ind = 1 gives the Pauli-X operator, ind = 2 gives the Pauli-Y operator, ind = 3 gives the Pauli-Z operator, and ind = 0 gives the identity operator. Alternatively, ind can be set to “I”, “X”, “Y”, or “Z” (case insensitive) to indicate the Pauli identity, X, Y, or Z operator.

The 2-by-2 Pauli matrices are defined as the following matrices:

\[\begin{split}\begin{equation} \begin{aligned} X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}, \quad Y = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}, \quad Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}, \quad I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}. \end{aligned} \end{equation}\end{split}\]

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]])

References

[1] (1,2)

Wikipedia. Pauli matrices. https://en.wikipedia.org/wiki/Pauli_matrices.

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