def __init__(self, coeffs, observables, simplify=False):
if len(coeffs) != len(observables):
raise ValueError(
"Could not create valid Hamiltonian; "
"number of coefficients and operators does not match.")
if any(np.imag(coeffs) != 0):
raise ValueError("Could not create valid Hamiltonian; "
"coefficients are not real-valued.")
for obs in observables:
if not isinstance(obs, Observable):
raise ValueError(
"Could not create circuits. Some or all observables are not valid."
)
self._coeffs = list(coeffs)
self._ops = list(observables)
self.data = []
self.return_type = None
if simplify:
self.simplify()
self.queue()
def mt(*params):
state = qnode(*params)
rqnode = lambda *params: np.real(qnode(*params))
iqnode = lambda *params: np.imag(qnode(*params))
rjac = qml.jacobian(rqnode)(*params)
ijac = qml.jacobian(iqnode)(*params)
if isinstance(rjac, tuple):
out = []
for rc, ic in zip(rjac, ijac):
c = rc + 1j * ic
psidpsi = np.tensordot(np.conj(state), c, axes=([0], [0]))
out.append(
np.real(
np.tensordot(np.conj(c), c, axes=([0], [0])) -
np.tensordot(np.conj(psidpsi), psidpsi, axes=0)))
return tuple(out)
jac = rjac + 1j * ijac
psidpsi = np.tensordot(np.conj(state), jac, axes=([0], [0]))
return np.real(
np.tensordot(np.conj(jac), jac, axes=([0], [0])) -
np.tensordot(np.conj(psidpsi), psidpsi, axes=0))
n_samples = 100
coeffs = []
for i in range(n_samples):
weights = random_weights()
def f(x):
return np.array([quantum_model(weights, x_) for x_ in x])
coeffs_sample = fourier_coefficients(f, n_coeffs)
coeffs.append(coeffs_sample)
coeffs = np.array(coeffs)
coeffs_real = np.real(coeffs)
coeffs_imag = np.imag(coeffs)
######################################################################
# Let's plot the real vs. the imaginary part of the coefficients. As a
# sanity check, the :math:`c_0` coefficient should be real, and therefore
# have no contribution on the y-axis.
#
n_coeffs = len(coeffs_real[0])
fig, ax = plt.subplots(1, n_coeffs, figsize=(15, 4))
for idx, ax_ in enumerate(ax):
ax_.set_title(r"$c_{}$".format(idx))
ax_.scatter(coeffs_real[:, idx],
coeffs_imag[:, idx],