def Unitary2Chi(U, B = None):
"""
map unitary process U onto the according chi matrix
option: provide an orthogonal basis B instead of the standard
Pauli basis for the chi matrix
"""
NumberOfQubits = int(np.log2(U.shape[0]))
chidim = 4**NumberOfQubits
a = proctom.getopbase()
A = a
for k in xrange(NumberOfQubits-1):
A = proctom.baseappend(A,a)
lam = np.zeros(chidim, dtype=complex)
for k in xrange(chidim):
lam[k] = np.trace(np.dot(A[k].transpose().conjugate(),U))/2**NumberOfQubits
chi = np.zeros((chidim,chidim), dtype=complex)
for k in xrange(chidim):
for l in xrange(chidim):
chi[k,l]=lam[k]*lam[l].conjugate()
return chi
def chirotinfidel(rot_vector, ideal_chi, my_chi,return_chi=False):
"The infidelity function"
NrOfQubits = int(len(rot_vector)/3)
# rz = expm(-1j*pi/2 * rot_vector[0] * X)
# ry = expm(-1j*pi/2 * rot_vector[1] * Y)
# rx = expm(-1j*pi/2 * rot_vector[2] * X)
R = lambda rot_vector: np.dot(expm(-1j*pi/2 * rot_vector[2] * X),np.dot(expm(-1j*pi/2 * rot_vector[1] * Y),expm(-1j*pi/2 * rot_vector[0] * X)))
Rtot = 1
AllPaulis = [1]
for k in xrange(NrOfQubits):
Rtot = npml.kron(Rtot, R(rot_vector[3*k:3*k+3]))
AllPaulis = proctom.baseappend(AllPaulis, Paulis)
k = 0
l = 0
res1 = np.zeros((4**NrOfQubits,4**NrOfQubits),dtype=np.complex)
for p_matrix in AllPaulis:
RA = np.dot(Rtot, p_matrix)
for p_matrix2 in AllPaulis:
res0 = np.dot(p_matrix2.conj().T, RA) / 2**NrOfQubits
res1[k,l] = np.trace(res0)
l += 1
l = 0
k += 1
chirot = np.dot(res1.T,np.dot(my_chi, res1.conj()))
# IF1 = np.real(1-np.trace(np.dot(ideal_chi,chirot)))
# IF1 = np.real(1-np.sum(ideal_chi*chirot.transpose()))
# IF = np.real(1-np.diag(np.dot(ideal_chi,chirot)))
IF = np.real(1-np.sum(ideal_chi*chirot.transpose(),axis=1))
if return_chi:
return chirot
else:
return IF
def Unitary2Chi(U, B=None):
"""
map unitary process U onto the according chi matrix
option: provide an orthogonal basis B instead of the standard
Pauli basis for the chi matrix
"""
NumberOfQubits = int(np.log2(U.shape[0]))
chidim = 4**NumberOfQubits
a = proctom.getopbase()
A = a
for k in xrange(NumberOfQubits - 1):
A = proctom.baseappend(A, a)
lam = np.zeros(chidim, dtype=complex)
for k in xrange(chidim):
lam[k] = np.trace(np.dot(A[k].transpose().conjugate(),
U)) / 2**NumberOfQubits
chi = np.zeros((chidim, chidim), dtype=complex)
for k in xrange(chidim):
for l in xrange(chidim):
chi[k, l] = lam[k] * lam[l].conjugate()
return chi
