def rand_ket(N, density=1, dims=None):
"""Creates a random Nx1 sparse ket vector.
Parameters
----------
N : int
Number of rows for output quantum operator.
density : float
Density between [0,1] of output ket state.
dims : list
Left-dimensions of quantum object. Used for specifying
tensor structure. Default is dims=[[N]].
Returns
-------
oper : qobj
Nx1 ket state quantum operator.
"""
if dims:
_check_ket_dims(dims, N)
X = sp.rand(N, 1, density, format="csr")
X.data = X.data - 0.5
Y = X.copy()
Y.data = 1.0j * (np.random.random(len(X.data)) - 0.5)
X = X + Y
X.sort_indices()
X = Qobj(X)
if dims:
return Qobj(X / X.norm(), dims=[dims, [1]], shape=[N, 1])
else:
return Qobj(X / X.norm())
def rand_ket(N, density=1, dims=None):
"""Creates a random Nx1 sparse ket vector.
Parameters
----------
N : int
Number of rows for output quantum operator.
density : float
Density between [0,1] of output ket state.
dims : list
Left-dimensions of quantum object. Used for specifying
tensor structure. Default is dims=[[N]].
Returns
-------
oper : qobj
Nx1 ket state quantum operator.
"""
if dims:
_check_ket_dims(dims, N)
X = sp.rand(N, 1, density, format='csr')
X.data = X.data - 0.5
Y = X.copy()
Y.data = 1.0j * (np.random.random(len(X.data)) - 0.5)
X = X + Y
X.sort_indices()
X = Qobj(X)
if dims:
return Qobj(X / X.norm(), dims=dims)
else:
return Qobj(X / X.norm())
def test_QobjNorm():
"Qobj norm"
# vector L2-norm test
N = 20
x = np.random.random(N) + 1j * np.random.random(N)
A = Qobj(x)
assert_equal(np.abs(A.norm() - la.norm(A.data.data, 2)) < 1e-12, True)
# vector max (inf) norm test
assert_equal(np.abs(A.norm("max") - la.norm(A.data.data, np.inf)) < 1e-12, True)
# operator frobius norm
x = np.random.random((N, N)) + 1j * np.random.random((N, N))
A = Qobj(x)
assert_equal(np.abs(A.norm("fro") - la.norm(A.full(), "fro")) < 1e-12, True)
def test_QobjNorm():
"Qobj norm"
# vector L2-norm test
N = 20
x = np.random.random(N) + 1j * np.random.random(N)
A = Qobj(x)
assert_equal(np.abs(A.norm() - la.norm(A.data.data, 2)) < 1e-12, True)
# vector max (inf) norm test
assert_equal(
np.abs(A.norm('max') - la.norm(A.data.data, np.inf)) < 1e-12, True)
# operator frobius norm
x = np.random.random((N, N)) + 1j * np.random.random((N, N))
A = Qobj(x)
assert_equal(
np.abs(A.norm('fro') - la.norm(A.full(), 'fro')) < 1e-12, True)
def test_QobjNorm():
"Qobj norm"
# vector L2-norm test
N = 20
x = np.random.random(N) + 1j * np.random.random(N)
A = Qobj(x)
assert np.abs(A.norm() - la.norm(A.data.data, 2)) < 1e-12
# vector max (inf) norm test
assert np.abs(A.norm('max') - la.norm(A.data.data, np.inf)) < 1e-12
# operator frobius norm
x = np.random.random((N, N)) + 1j * np.random.random((N, N))
A = Qobj(x)
assert np.abs(A.norm('fro') - la.norm(A.full(), 'fro')) < 1e-12
# operator trace norm
a = rand_herm(10, 0.25)
assert np.allclose(a.norm(), (a * a.dag()).sqrtm().tr().real)
b = rand_herm(10, 0.25) - 1j * rand_herm(10, 0.25)
assert np.allclose(b.norm(), (b * b.dag()).sqrtm().tr().real)
def test_QobjNorm():
"Qobj norm"
# vector L2-norm test
N = 20
x = np.random.random(N) + 1j * np.random.random(N)
A = Qobj(x)
assert_equal(np.abs(A.norm() - la.norm(A.data.data, 2)) < 1e-12, True)
# vector max (inf) norm test
assert_equal(
np.abs(A.norm('max') - la.norm(A.data.data, np.inf)) < 1e-12, True)
# operator frobius norm
x = np.random.random((N, N)) + 1j * np.random.random((N, N))
A = Qobj(x)
assert_equal(
np.abs(A.norm('fro') - la.norm(A.full(), 'fro')) < 1e-12, True)
# operator trace norm
a = rand_herm(10,0.25)
assert_almost_equal(a.norm(), (a*a.dag()).sqrtm().tr().real)
b = rand_herm(10,0.25) - 1j*rand_herm(10,0.25)
assert_almost_equal(b.norm(), (b*b.dag()).sqrtm().tr().real)
def rand_ket(N=None, density=1, dims=None, seed=None):
"""Creates a random Nx1 sparse ket vector.
Parameters
----------
N : int
Number of rows for output quantum vector.
If None, N is deduced from dims.
density : float
Density between [0,1] of output ket state.
dims : list
Dimensions of quantum object. Used for specifying
tensor structure. Default is dims=[[N],[1]].
seed : int
Seed for the random number generator.
Returns
-------
oper : qobj
Nx1 ket quantum state vector.
Raises
-------
ValueError
If neither `N` or `dims` are specified.
"""
if seed is not None:
np.random.seed(seed=seed)
if N is None and dims is None:
raise ValueError('Specify either the number of rows of state vector'
'(N) or dimensions of quantum object (dims)')
if N is not None and dims:
_check_dims(dims, N, 1)
elif dims:
N = np.prod(dims[0])
_check_dims(dims, N, 1)
else:
dims = [[N], [1]]
X = sp.rand(N, 1, density, format='csr')
while X.nnz == 0:
# ensure that the ket is not all zeros.
X = sp.rand(N, 1, density + 1 / N, format='csr')
X.data = X.data - 0.5
Y = X.copy()
Y.data = 1.0j * (np.random.random(len(X.data)) - 0.5)
X = X + Y
X.sort_indices()
X = Qobj(X)
return Qobj(X / X.norm(), dims=dims)
def rand_ket(N=0, density=1, dims=None, seed=None):
"""Creates a random Nx1 sparse ket vector.
Parameters
----------
N : int
Number of rows for output quantum operator.
If None or 0, N is deduced from dims.
density : float
Density between [0,1] of output ket state.
dims : list
Dimensions of quantum object. Used for specifying
tensor structure. Default is dims=[[N],[1]].
Returns
-------
oper : qobj
Nx1 ket state quantum operator.
"""
if seed is not None:
np.random.seed(seed=seed)
if N and dims:
_check_dims(dims, N, 1)
elif dims:
N = prod(dims[0])
_check_dims(dims, N, 1)
else:
dims = [[N],[1]]
X = sp.rand(N, 1, density, format='csr')
while X.nnz == 0:
# ensure that the ket is not all zeros.
X = sp.rand(N, 1, density+1/N, format='csr')
X.data = X.data - 0.5
Y = X.copy()
Y.data = 1.0j * (np.random.random(len(X.data)) - 0.5)
X = X + Y
X.sort_indices()
X = Qobj(X)
return Qobj(X / X.norm(), dims=dims)
def test_tidyup_default(tol):
with auto_tidyup_tol(tol):
small = Qobj(1) * 1e-10
assert (small.norm() == 0) == (tol > 1e-10)