toqito.rand.random_unitary

Generates a random unitary matrix.

Module Contents

toqito.rand.random_unitary.random_unitary(dim, is_real=False, seed=None)

Generate a random unitary or orthogonal matrix [@Ozols_2009_RandU].

Calculates a random unitary matrix (if is_real = False) or a random real orthogonal matrix (if is_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.

```python exec=”1” source=”above” session=”complex_dm” from toqito.rand import random_unitary

complex_dm = random_unitary(2)

print(complex_dm) ```

We can verify that this is in fact a valid unitary matrix using the is_unitary function from |toqito⟩ as follows

```python exec=”1” source=”above” session=”complex_dm” from toqito.matrix_props import is_unitary

print(is_unitary(complex_dm)) ```

We can also generate random unitary matrices that are real-valued as follows.

```python exec=”1” source=”above” session=”real_dm” from toqito.rand import random_unitary

real_dm = random_unitary(2, True)

print(real_dm) ```

Again, verifying that this is a valid unitary matrix can be done as follows.

```python exec=”1” source=”above” session=”real_dm” from toqito.matrix_props import is_unitary

print(is_unitary(real_dm)) ```

We may also generate unitaries such that the dimension argument provided is a list as opposed to an int. Here is an example of a random unitary matrix of dimension (4).

```python exec=”1” source=”above” session=”mat” from toqito.rand import random_unitary

mat = random_unitary([4, 4], True)

print(mat) ```

As before, we can verify that this matrix generated is a valid unitary matrix.

```python exec=”1” source=”above” session=”mat” from toqito.matrix_props import is_unitary

print(is_unitary(mat)) ```

It is also possible to pass a seed to this function for reproducibility.

```python exec=”1” source=”above” session=”seeded” from toqito.rand import random_unitary

seeded = random_unitary(2, seed=42)

print(seeded) ```

And once again, we can verify that this matrix generated is a valid unitary matrix.

```python exec=”1” source=”above” session=”seeded” from toqito.matrix_props import is_unitary

print(is_unitary(seeded)) ```

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.

• seed (int | None) – A seed used to instantiate numpy’s random number generator.

Returns:

A dim-by-dim random unitary matrix.

Return type:

numpy.ndarray