def wavefunction(self,
esys: Tuple[ndarray, ndarray],
which: int = 0,
phi_grid: 'Grid1d' = None) -> storage.WaveFunction:
"""Returns a fluxonium wave function in `phi` basis
Parameters
----------
esys:
eigenvalues, eigenvectors
which:
index of desired wave function (default value = 0)
phi_grid:
used for setting a custom grid for phi; if None use self._default_grid
"""
if esys is None:
evals_count = max(which + 1, 3)
evals, evecs = self.eigensys(evals_count)
else:
evals, evecs = esys
dim = self.hilbertdim()
phi_grid = phi_grid or self._default_grid
phi_basis_labels = phi_grid.make_linspace()
wavefunc_osc_basis_amplitudes = evecs[:, which]
phi_wavefunc_amplitudes = np.zeros(phi_grid.pt_count,
dtype=np.complex_)
phi_osc = self.phi_osc()
for n in range(dim):
phi_wavefunc_amplitudes += wavefunc_osc_basis_amplitudes[n] \
* osc.harm_osc_wavefunction(n, phi_basis_labels, phi_osc)
return storage.WaveFunction(basis_labels=phi_basis_labels,
amplitudes=phi_wavefunc_amplitudes,
energy=evals[which])
def wavefunction(
self,
esys: Tuple[ndarray, ndarray] = None,
which: int = 0,
phi_grid: Grid1d = None,
) -> WaveFunction:
"""Return the transmon wave function in phase basis. The specific index of the wavefunction is `which`.
`esys` can be provided, but if set to `None` then it is calculated on the fly.
Parameters
----------
esys:
if None, the eigensystem is calculated on the fly; otherwise, the provided eigenvalue, eigenvector arrays
as obtained from `.eigensystem()` are used
which:
eigenfunction index (default value = 0)
phi_grid:
used for setting a custom grid for phi; if None use self._default_grid
"""
if esys is None:
evals_count = max(which + 1, 3)
evals, evecs = self.eigensys(evals_count)
else:
evals, evecs = esys
n_wavefunc = self.numberbasis_wavefunction(esys, which=which)
phi_grid = phi_grid or self._default_grid
phi_basis_labels = phi_grid.make_linspace()
phi_wavefunc_amplitudes = np.empty(phi_grid.pt_count,
dtype=np.complex_)
for k in range(phi_grid.pt_count):
phi_wavefunc_amplitudes[k] = (
1j**which / math.sqrt(2 * np.pi)) * np.sum(
n_wavefunc.amplitudes *
np.exp(1j * phi_basis_labels[k] * n_wavefunc.basis_labels))
return storage.WaveFunction(
basis_labels=phi_basis_labels,
amplitudes=phi_wavefunc_amplitudes,
energy=evals[which],
)
def numberbasis_wavefunction(self,
esys: Tuple[ndarray, ndarray] = None,
which: int = 0) -> WaveFunction:
"""Return the transmon wave function in number basis. The specific index of the wave function to be returned is
`which`.
Parameters
----------
esys:
if `None`, the eigensystem is calculated on the fly; otherwise, the provided eigenvalue, eigenvector arrays
as obtained from `.eigensystem()`, are used (default value = None)
which:
eigenfunction index (default value = 0)
"""
if esys is None:
evals_count = max(which + 1, 3)
esys = self.eigensys(evals_count)
evals, evecs = esys
n_vals = np.arange(-self.ncut, self.ncut + 1)
return storage.WaveFunction(n_vals, evecs[:, which], evals[which])