matrices.clock
Clock matrix.
Module Contents
Functions
|
Produce clock matrix [1]. |
- matrices.clock.clock(dim)
Produce clock matrix [1].
Returns the clock matrix of dimension
dim
described in [1]. The clock matrix generates the followingdim
-by-dim
matrix\[\begin{split}\Sigma_{1, d} = \begin{pmatrix} 1 & 0 & 0 & \ldots & 0 \\ 0 & \omega & 0 & \ldots & 0 \\ 0 & 0 & \omega^2 & \ldots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \ldots & \omega^{d-1} \end{pmatrix}\end{split}\]where \(\omega\) is the n-th primitive root of unity.
The clock matrix is primarily used in the construction of the generalized Pauli operators.
Examples
The clock matrix generated from \(d = 3\) yields the following matrix:
\[\begin{split}\Sigma_{1, 3} = \begin{pmatrix} 1 & 0 & 0 \\ 0 & \omega & 0 \\ 0 & 0 & \omega^2 \end{pmatrix}\end{split}\]>>> from toqito.matrices import clock >>> clock(3) [[ 1. +0.j , 0. +0.j , 0. +0.j ], [ 0. +0.j , -0.5+0.8660254j, 0. +0.j ], [ 0. +0.j , 0. +0.j , -0.5-0.8660254j]]
References
- Parameters:
dim (int) – Dimension of the matrix.
- Returns:
dim
-by-dim
clock matrix.- Return type:
numpy.ndarray