def vector(evo):
assert len(evo)
(time,dop) = evo[0]
assert dop.shape[0] == dop.shape[1] == 2
# bloch vector coordinates
vector = None
for i in range(0,len(evo)):
(time,dop) = evo[i]
assert (dop == numpy.conjugate(numpy.transpose(dop))).all()
x = hs.dot(pauli.X,dop)
y = hs.dot(pauli.Y,dop)
z = hs.dot(pauli.Z,dop)
entry = numpy.array([x,y,z])
if vector is None:
vector = entry
else:
vector = numpy.vstack([vector,entry])
return vector
def hermitian_subspace_generator(generator_func, n):
"""
return the generator acting on the real Hermitian subspace of n*n complex matrices
generator_func function accepting a n*n matrix and returning the
time derivative for the given input
n system's order
"""
assert generator_func
assert n>0
basis = hermitian_subspace_basis(n)
_map = numpy.zeros((n*n,n*n))
row = 0
col = 0
for row in range(0, n*n):
for col in range(0, n*n):
_map[row][col] = hs.dot(basis[col], generator_func(basis[row]))
return _map
def bloch_vector(signal):
assert len(signal)
(time,dop) = signal[0]
assert dop.shape[0] == dop.shape[1] == 2
import pauli
import hs
x = []
y = []
z = []
for i in range(0,len(signal)):
(time,dop) = signal[i]
# coordinates in the basis I, X, Y e Z
i_tmp = hs.dot(pauli.I,dop)
x_tmp = hs.dot(pauli.X,dop)
y_tmp = hs.dot(pauli.Y,dop)
z_tmp = hs.dot(pauli.Z,dop)
# print i_tmp, x_tmp, y_tmp, z_tmp
# assert numpy.imag(x_tmp) == numpy.imag(y_tmp) == numpy.imag(z_tmp) == 0.
# print 'dop', dop
# print 'sum', (pauli.I*i_tmp + x_tmp*pauli.X+y_tmp*pauli.Y+z_tmp*pauli.Z)/2.
# assert (pauli.I*i_tmp + x_tmp*pauli.X+y_tmp*pauli.Y+z_tmp*pauli.Z == dop).all()
x.append(numpy.real(x_tmp))
y.append(numpy.real(y_tmp))
z.append(numpy.real(z_tmp))
# x = numpy.array(x)
# y = numpy.array(y)
# z = numpy.array(z)
# print x
# print y
# print z
# print x.shape
# print y.shape
# print z.shape
from mpl_toolkits.mplot3d import Axes3D
import pylab
mpl.rcParams['legend.fontsize'] = 10
fig = pylab.figure()
ax = Axes3D(fig)
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
sx = 1 * np.outer(np.cos(u), np.sin(v))
sy = 1 * np.outer(np.sin(u), np.sin(v))
sz = 1 * np.outer(np.ones(np.size(u)), np.cos(v))
ax.plot_surface(sx, sy, sz, rstride=25, cstride=25, color='b', alpha=0.05)
pylab.hold(True)
ax.plot(x, y, z, label='parametric curve')
ax.legend()
pylab.show()