def random_orthogonal(
dim: int,
*,
random_state: value.RANDOM_STATE_LIKE = None) -> np.ndarray:
"""Returns a random orthogonal matrix distributed with Haar measure.
Args:
dim: The width and height of the matrix.
random_state: A seed (int) or `np.random.RandomState` class to use when
generating random values. If not set, defaults to using the module
methods in `np.random`.
Returns:
The sampled orthogonal matrix.
References:
'How to generate random matrices from the classical compact groups'
http://arxiv.org/abs/math-ph/0609050
"""
random_state = value.parse_random_state(random_state)
m = random_state.randn(dim, dim)
q, r = np.linalg.qr(m)
d = np.diag(r)
return q * (d / abs(d))
def random_superposition(dim: int,
*,
random_state: value.RANDOM_STATE_LIKE = None
) -> np.ndarray:
"""Returns a random unit-length vector from the uniform distribution.
Args:
dim: The dimension of the vector.
Returns:
The sampled unit-length vector.
"""
random_state = value.parse_random_state(random_state)
state_vector = random_state.randn(dim).astype(complex)
state_vector += 1j * random_state.randn(dim)
state_vector /= np.linalg.norm(state_vector)
return state_vector
def random_superposition(
dim: int,
*,
random_state: value.RANDOM_STATE_LIKE = None) -> np.ndarray:
"""Returns a random unit-length vector from the uniform distribution.
Args:
dim: The dimension of the vector.
random_state: A seed (int) or `np.random.RandomState` class to use when
generating random values. If not set, defaults to using the module
methods in `np.random`.
Returns:
The sampled unit-length vector.
"""
random_state = value.parse_random_state(random_state)
state_vector = random_state.randn(dim).astype(complex)
state_vector += 1j * random_state.randn(dim)
state_vector /= np.linalg.norm(state_vector)
return state_vector
def random_unitary(dim: int, *,
random_state: value.RANDOM_STATE_LIKE = None) -> np.ndarray:
"""Returns a random unitary matrix distributed with Haar measure.
Args:
dim: The width and height of the matrix.
random_state: A seed to use for random number generation.
Returns:
The sampled unitary matrix.
References:
'How to generate random matrices from the classical compact groups'
http://arxiv.org/abs/math-ph/0609050
"""
random_state = value.parse_random_state(random_state)
z = (random_state.randn(dim, dim) + 1j * random_state.randn(dim, dim))
q, r = np.linalg.qr(z)
d = np.diag(r)
return q * (d / abs(d))
def random_density_matrix(
dim: int,
*,
random_state: value.RANDOM_STATE_LIKE = None) -> np.ndarray:
"""Returns a random density matrix distributed with Hilbert-Schmidt measure.
Args:
dim: The width and height of the matrix.
random_state: A seed to use for random number generation.
Returns:
The sampled density matrix.
Reference:
'Random Bures mixed states and the distribution of their purity'
https://arxiv.org/abs/0909.5094
"""
random_state = value.parse_random_state(random_state)
mat = random_state.randn(dim, dim) + 1j * random_state.randn(dim, dim)
mat = mat @ mat.T.conj()
return mat / np.trace(mat)
def random_orthogonal(dim: int, *, random_state: value.RANDOM_STATE_LIKE = None
) -> np.ndarray:
"""Returns a random orthogonal matrix distributed with Haar measure.
Args:
dim: The width and height of the matrix.
Returns:
The sampled orthogonal matrix.
References:
'How to generate random matrices from the classical compact groups'
http://arxiv.org/abs/math-ph/0609050
"""
random_state = value.parse_random_state(random_state)
m = random_state.randn(dim, dim)
q, r = np.linalg.qr(m)
d = np.diag(r)
return q * (d / abs(d))