def test_vectorize(self):
mat = [[1, 2], [3, 4]]
col = [1, 3, 2, 4]
row = [1, 2, 3, 4]
paul = [5, 5, -1j, -3]
test_pass = (np.linalg.norm(vectorize(mat) - col) == 0 and
np.linalg.norm(vectorize(mat, method='col') - col) == 0 and
np.linalg.norm(vectorize(mat, method='row') - row) == 0 and
np.linalg.norm(vectorize(mat, method='pauli') - paul) == 0)
self.assertTrue(test_pass)
def test_vectorize(self):
mat = [[1, 2], [3, 4]]
col = [1, 3, 2, 4]
row = [1, 2, 3, 4]
paul = [5, 5, -1j, -3]
test_pass = np.linalg.norm(vectorize(mat) - col) == 0 and \
np.linalg.norm(vectorize(mat, method='col') - col) == 0 and \
np.linalg.norm(vectorize(mat, method='row') - row) == 0 and \
np.linalg.norm(vectorize(mat, method='pauli') - paul) == 0
self.assertTrue(test_pass)
def __tomo_basis_matrix(meas_basis):
"""Return a matrix of vectorized measurement operators.
Args:
meas_basis(list(array_like)): measurement operators [M_j].
Returns:
The operators S = sum_j |j><M_j|.
"""
n = len(meas_basis)
d = meas_basis[0].size
S = np.array([vectorize(m).conj() for m in meas_basis])
return S.reshape(n, d)
def __tomo_basis_matrix(meas_basis):
"""Return a matrix of vectorized measurement operators.
Args:
meas_basis(list(array_like)): measurement operators [M_j].
Returns:
The operators S = sum_j |j><M_j|.
"""
n = len(meas_basis)
d = meas_basis[0].size
S = np.array([vectorize(m).conj() for m in meas_basis])
return S.reshape(n, d)
def __tomo_linear_inv(freqs, ops, weights=None, trace=None):
"""
Reconstruct a matrix through linear inversion.
Args:
freqs (list[float]): list of observed frequences.
ops (list[np.array]): list of corresponding projectors.
weights (list[float] or array_like):
weights to be used for weighted fitting.
trace (float or None): trace of returned operator.
Returns:
numpy.array: A numpy array of the reconstructed operator.
"""
# get weights matrix
if weights is not None:
W = np.array(weights)
if W.ndim == 1:
W = np.diag(W)
# Get basis S matrix
S = np.array([vectorize(m).conj()
for m in ops]).reshape(len(ops), ops[0].size)
if weights is not None:
S = np.dot(W, S) # W.S
# get frequencies vec
v = np.array(freqs) # |f>
if weights is not None:
v = np.dot(W, freqs) # W.|f>
Sdg = S.T.conj() # S^*.W^*
inv = np.linalg.pinv(np.dot(Sdg, S)) # (S^*.W^*.W.S)^-1
# linear inversion of freqs
ret = devectorize(np.dot(inv, np.dot(Sdg, v)))
# renormalize to input trace value
if trace is not None:
ret = trace * ret / np.trace(ret)
return ret
def __tomo_linear_inv(freqs, ops, weights=None, trace=None):
"""
Reconstruct a matrix through linear inversion.
Args:
freqs (list[float]): list of observed frequences.
ops (list[np.array]): list of corresponding projectors.
weights (list[float] or array_like):
weights to be used for weighted fitting.
trace (float or None): trace of returned operator.
Returns:
numpy.array: A numpy array of the reconstructed operator.
"""
# get weights matrix
if weights is not None:
W = np.array(weights)
if W.ndim == 1:
W = np.diag(W)
# Get basis S matrix
S = np.array([vectorize(m).conj()
for m in ops]).reshape(len(ops), ops[0].size)
if weights is not None:
S = np.dot(W, S) # W.S
# get frequencies vec
v = np.array(freqs) # |f>
if weights is not None:
v = np.dot(W, freqs) # W.|f>
Sdg = S.T.conj() # S^*.W^*
inv = np.linalg.pinv(np.dot(Sdg, S)) # (S^*.W^*.W.S)^-1
# linear inversion of freqs
ret = devectorize(np.dot(inv, np.dot(Sdg, v)))
# renormalize to input trace value
if trace is not None:
ret = trace * ret / np.trace(ret)
return ret
