toqito.matrix_ops.unvec

Unvec operation is used to perform the unvec operation on a vector.

Module Contents

toqito.matrix_ops.unvec.unvec(vector, shape=None)

Perform the unvec operation on a vector to obtain a matrix [@Rigetti_2022_Forest].

Takes a column vector and transforms it into a shape[0]-by-shape[1] matrix. This operation is the inverse of vec operation in |toqito⟩.

For instance, for the following column vector

[

u = begin{pmatrix} 1 \ 3 \ 2 \ 4 end{pmatrix},

]

it holds that

[

text{unvec}(u) = begin{pmatrix}

1 & 2 \ 3 & 4

end{pmatrix}

]

More formally, the vec operation is defined by

[

text{unvec}(e_a otimes e_b) = E_{a,b}

]

for all (a) and (b) where

[

E_{a,b}(c,d) = begin{cases}

1 & text{if} (c,d) = (a,b) \ 0 & text{otherwise}

end{cases}

]

for all (c) and (d) and where

[

e_a(b) = begin{cases}

1 & text{if} a = b \ 0 & text{if} a not= b

end{cases}

]

for all (a) and (b).

This function has been adapted from [@Rigetti_2022_Forest].

Examples

Consider the following vector

[

u = begin{pmatrix} 1 \ 3 \ 2 \ 4 end{pmatrix}

]

Performing the (text{unvec}) operation on (u) yields

[

text{unvec}(u) = begin{pmatrix} 1 & 2 \ 3 & 4 end{pmatrix}

]

```python exec=”1” source=”above” import numpy as np from toqito.matrix_ops import unvec

u = np.array([1, 2, 3, 4])

print(unvec(u)) ```

!!! See Also

[vec][toqito.matrix_ops.vec.vec]

Parameters:

• vector (numpy.ndarray) – A (shape[0] * shape[1])-by-1 numpy array.

• shape (list[int] | None) – The shape of the output matrix; by default, the matrix is assumed to be square.

Returns:

Returns a shape[0]-by-shape[1] matrix.

Return type:

numpy.ndarray