rand.random_unitary
¶
Generate random unitary.
Module Contents¶
Functions¶
|
Generate a random unitary or orthogonal matrix [1]. |
- rand.random_unitary.random_unitary(dim, is_real=False)¶
Generate a random unitary or orthogonal matrix [1].
Calculates a random unitary matrix (if
is_real = False
) or a random real orthogonal matrix (ifis_real = True
), uniformly distributed according to the Haar measure.Examples
We may generate a random unitary matrix. Here is an example of how we may be able to generate a random \(2\)-dimensional random unitary matrix with complex entries.
>>> from toqito.rand import random_unitary >>> complex_dm = random_unitary(2) >>> complex_dm array([[ 0.13764463+0.65538975j, 0.74246453+0.01626838j], [ 0.45776527+0.58478132j, -0.6072508 +0.28236187j]])
We can verify that this is in fact a valid unitary matrix using the
is_unitary
function fromtoqito
as follows>>> from toqito.matrix_props import is_unitary >>> is_unitary(complex_dm) True
We can also generate random unitary matrices that are real-valued as follows.
>>> from toqito.rand import random_unitary >>> real_dm = random_unitary(2, True) >>> real_dm array([[ 0.87766506, -0.47927449], [ 0.47927449, 0.87766506]])
Again, verifying that this is a valid unitary matrix can be done as follows.
>>> from toqito.matrix_props import is_unitary >>> is_unitary(real_dm) True
We may also generate unitaries such that the dimension argument provided is a
list
as opposed to anint
. Here is an example of a random unitary matrix of dimension \(4\).>>> from toqito.rand import random_unitary >>> mat = random_unitary([4, 4], True) >>> mat array([[ 0.49527332, 0.08749933, -0.16968586, 0.84749922], [ 0.68834418, -0.26695275, 0.62674543, -0.24921614], [ 0.38614979, -0.438767 , -0.7417619 , -0.32887862], [ 0.36300822, 0.85355938, -0.16788735, -0.33387909]])
As before, we can verify that this matrix generated is a valid unitary matrix.
>>> from toqito.matrix_props import is_unitary >>> is_unitary(mat) True
References
- Parameters:
dim (list[int] | int) – The number of rows (and columns) of the unitary matrix.
is_real (bool) – Boolean denoting whether the returned matrix has real entries or not. Default is
False
.
- Returns:
A
dim
-by-dim
random unitary matrix.- Return type:
numpy.ndarray