# Random matrices¶

This submodule provides access to utility functions to generate random unitary, symplectic and covariance matrices.

randnc(*arg)[source]

Normally distributed array of random complex numbers.

random_banded_interferometer(N, w, top_one_init=True, real=False)[source]

Generates a banded unitary matrix.

Parameters
• N (int) – number of modes

• w (int) – bandwidth

• top_one_init (bool) – if True places a 1times1 interferometer in the top-left-most block of the first matrix in the product

• real (bool) – return a random real orthogonal matrix

Returns

random $$N\times N$$ unitary with the specified block structure

Return type

array

random_block_interferometer(N, top_one=True, real=False)[source]

Generates a random interferometer with blocks of at most size 2.

Parameters
• N (int) – number of modes

• top_one (bool) – if True places a 1times1 interferometer in the top-left most block

• real (bool) – return a random real orthogonal matrix

Returns

random $$N\times N$$ unitary with the specified block structure

Return type

array

random_covariance(N, hbar=2, pure=False, block_diag=False)[source]

Random covariance matrix.

Parameters
• N (int) – number of modes

• hbar (float) – the value of $$\hbar$$ to use in the definition of the quadrature operators $$x$$ and $$p$$

• pure (bool) – If True, a random covariance matrix corresponding to a pure state is returned.

• block_diag (bool) – If True, uses passive Gaussian transformations that are orthogonal instead of unitary. This implies that the positions $$x$$ do not mix with the momenta $$p$$ and thus the covariance matrix is block diagonal.

Returns

random $$2N\times 2N$$ covariance matrix

Return type

array

random_interferometer(N, real=False)[source]

Random unitary matrix representing an interferometer. For more details, see [].

Parameters
• N (int) – number of modes

• real (bool) – return a random real orthogonal matrix

Returns

random $$N\times N$$ unitary distributed with the Haar measure

Return type

array

random_symplectic(N, passive=False, block_diag=False, scale=1.0)[source]

Random symplectic matrix representing a Gaussian transformation.

The squeezing parameters $$r$$ for active transformations are randomly sampled from the standard normal distribution, while passive transformations are randomly sampled from the Haar measure. Note that for the Symplectic group there is no notion of Haar measure since this is group is not compact.

Parameters
• N (int) – number of modes

• passive (bool) – If True, returns a passive Gaussian transformation (i.e., one that preserves photon number). If False, returns an active transformation.

• block_diag (bool) – If True, uses passive Gaussian transformations that are orthogonal instead of unitary. This implies that the positions $$q$$ do not mix with the momenta $$p$$ and thus the symplectic operator is block diagonal

• scale (float) – Sets the scale of the random values used as squeezing parameters. They will range from 0 to $$\sqrt{2}\texttt{scale}$$

Returns

random $$2N\times 2N$$ symplectic matrix

Return type

array