def wavefunction(
self,
esys: Tuple[ndarray, ndarray] = None,
which: int = 0,
phi_grid: discretization.Grid1d = None,
) -> storage.WaveFunctionOnGrid:
"""
Return a flux qubit wave function in phi1, phi2 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
"""
evals_count = max(which + 1, 3)
if esys is None:
_, evecs = self.eigensys(evals_count)
else:
_, evecs = esys
phi_grid = phi_grid or self._default_grid
dim = 2 * self.ncut + 1
state_amplitudes = np.reshape(evecs[:, which], (dim, dim))
n_vec = np.arange(-self.ncut, self.ncut + 1)
phi_vec = phi_grid.make_linspace()
a_1_phi = np.exp(1j * np.outer(phi_vec, n_vec)) / (2 * np.pi) ** 0.5
a_2_phi = a_1_phi.T
wavefunc_amplitudes = np.matmul(a_1_phi, state_amplitudes)
wavefunc_amplitudes = np.matmul(wavefunc_amplitudes, a_2_phi)
wavefunc_amplitudes = spec_utils.standardize_phases(wavefunc_amplitudes)
grid2d = discretization.GridSpec(
np.asarray(
[
[phi_grid.min_val, phi_grid.max_val, phi_grid.pt_count],
[phi_grid.min_val, phi_grid.max_val, phi_grid.pt_count],
]
)
)
return storage.WaveFunctionOnGrid(grid2d, wavefunc_amplitudes)
def wavefunction(
self,
esys: Tuple[ndarray, ndarray] = None,
which: int = 0,
theta_grid: Grid1d = None,
) -> WaveFunctionOnGrid:
"""Returns a zero-pi wave function in `phi`, `theta` basis
Parameters
----------
esys:
eigenvalues, eigenvectors
which:
index of desired wave function (default value = 0)
theta_grid:
used for setting a custom grid for theta; if None use self._default_grid
"""
evals_count = max(which + 1, 3)
if esys is None:
_, evecs = self.eigensys(evals_count)
else:
_, evecs = esys
theta_grid = theta_grid or self._default_grid
dim_theta = 2 * self.ncut + 1
state_amplitudes = evecs[:, which].reshape(self.grid.pt_count, dim_theta)
# Calculate psi_{phi, theta} = sum_n state_amplitudes_{phi, n} A_{n, theta}
# where a_{n, theta} = 1/sqrt(2 pi) e^{i n theta}
n_vec = np.arange(-self.ncut, self.ncut + 1)
theta_vec = theta_grid.make_linspace()
a_n_theta = np.exp(1j * np.outer(n_vec, theta_vec)) / (2 * np.pi) ** 0.5
wavefunc_amplitudes = np.matmul(state_amplitudes, a_n_theta).T
wavefunc_amplitudes = spec_utils.standardize_phases(wavefunc_amplitudes)
grid2d = discretization.GridSpec(
np.asarray(
[
[self.grid.min_val, self.grid.max_val, self.grid.pt_count],
[theta_grid.min_val, theta_grid.max_val, theta_grid.pt_count],
]
)
)
return storage.WaveFunctionOnGrid(grid2d, wavefunc_amplitudes)
def wavefunction(self,
esys=None,
which=0,
phi_grid=None,
zeta_grid=None,
theta_grid=None) -> WaveFunctionOnGrid:
"""
Return a 3D wave function in :math:`\\phi, \\zeta, \\theta` basis
Parameters
----------
esys: ndarray, ndarray
eigenvalues, eigenvectors
which: int, optional
index of desired wave function (default value = 0)
phi_grid: Grid1d, option
used for setting a custom grid for phi; if None use self._default_phi_grid
zeta_grid: Grid1d, option
used for setting a custom grid for zeta; if None use
self._default_zeta_grid
theta_grid: Grid1d, option
used for setting a custom grid for theta; if None use
self._default_theta_grid
"""
evals_count = max(which + 1, 3)
if esys is None:
_, evecs = self.eigensys(evals_count)
else:
_, evecs = esys
phi_grid = phi_grid or self._default_phi_grid
zeta_grid = zeta_grid or self._default_zeta_grid
theta_grid = theta_grid or self._default_theta_grid
phi_basis_labels = phi_grid.make_linspace()
zeta_basis_labels = zeta_grid.make_linspace()
theta_basis_labels = theta_grid.make_linspace()
wavefunc_basis_amplitudes = evecs[:, which].reshape(
self._dim_phi(), self._dim_zeta(), self._dim_theta())
wavefunc_amplitudes = np.zeros(
(phi_grid.pt_count, zeta_grid.pt_count, theta_grid.pt_count),
dtype=np.complex_,
)
for i in range(self._dim_phi()):
for j in range(self._dim_zeta()):
for k in range(self._dim_theta()):
n_phi, n_zeta, n_theta = i, j, k - self.ncut
phi_wavefunc_amplitudes = osc.harm_osc_wavefunction(
n_phi, phi_basis_labels, self.phi_osc())
zeta_wavefunc_amplitudes = osc.harm_osc_wavefunction(
n_zeta, zeta_basis_labels, self.zeta_osc())
theta_wavefunc_amplitudes = (
np.exp(-1j * n_theta * theta_basis_labels) /
(2 * np.pi)**0.5)
wavefunc_amplitudes += wavefunc_basis_amplitudes[
i, j, k] * np.tensordot(
np.tensordot(phi_wavefunc_amplitudes,
zeta_wavefunc_amplitudes, 0),
theta_wavefunc_amplitudes,
0,
)
grid3d = discretization.GridSpec(
np.asarray([
[phi_grid.min_val, phi_grid.max_val, phi_grid.pt_count],
[zeta_grid.min_val, zeta_grid.max_val, zeta_grid.pt_count],
[theta_grid.min_val, theta_grid.max_val, theta_grid.pt_count],
]))
return storage.WaveFunctionOnGrid(grid3d, wavefunc_amplitudes)