def plot_potential(self,
phi_grid: discretization.Grid1d = None,
contour_vals: ndarray = None,
**kwargs) -> Tuple[Figure, Axes]:
"""
Draw contour plot of the potential energy.
Parameters
----------
phi_grid:
used for setting a custom grid for phi; if None use self._default_grid
contour_vals:
specific contours to draw
**kwargs:
plot options
"""
phi_grid = phi_grid or self._default_grid
x_vals = y_vals = phi_grid.make_linspace()
if "figsize" not in kwargs:
kwargs["figsize"] = (5, 5)
return plot.contours(x_vals,
y_vals,
self.potential,
contour_vals=contour_vals,
**kwargs)
def plot_potential(self,
theta_grid: Grid1d = None,
contour_vals: Union[List[float], ndarray] = None,
**kwargs
) -> Tuple[Figure, Axes]:
"""Draw contour plot of the potential energy.
Parameters
----------
theta_grid:
used for setting a custom grid for theta; if None use self._default_grid
contour_vals:
**kwargs:
plotting parameters
"""
theta_grid = theta_grid or self._default_grid
x_vals = self.grid.make_linspace()
y_vals = theta_grid.make_linspace()
return plot.contours(x_vals,
y_vals,
self.potential,
contour_vals=contour_vals,
xlabel=r'$\phi$',
ylabel=r'$\theta$',
**kwargs)
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: 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 plot_wavefunction(
self,
which: Union[int, Iterable[int]] = 0,
mode: str = "real",
esys: Tuple[ndarray, ndarray] = None,
phi_grid: Grid1d = None,
scaling: float = None,
**kwargs,
) -> Tuple[Figure, Axes]:
"""Plot 1d phase-basis wave function(s). Must be overwritten by
higher-dimensional qubits like FluxQubits and ZeroPi.
Parameters
----------
which:
single index or tuple/list of integers indexing the wave function(s) to be
plotted.
If which is -1, all wavefunctions up to the truncation limit are plotted.
mode:
choices as specified in `constants.MODE_FUNC_DICT`
(default value = 'abs_sqr')
esys:
eigenvalues, eigenvectors
phi_grid:
used for setting a custom grid for phi; if None use self._default_grid
scaling:
custom scaling of wave function amplitude/modulus
**kwargs:
standard plotting option (see separate documentation)
"""
wavefunc_indices = process_which(which, self.truncated_dim)
if esys is None:
evals_count = max(wavefunc_indices) + 1
evals = self.eigenvals(evals_count=evals_count)
else:
evals, _ = esys
energies = evals[list(wavefunc_indices)]
phi_grid = phi_grid or self._default_grid
potential_vals = self.potential(phi_grid.make_linspace())
amplitude_modifier = constants.MODE_FUNC_DICT[mode]
wavefunctions = []
for wavefunc_index in wavefunc_indices:
phi_wavefunc = self.wavefunction(esys,
which=wavefunc_index,
phi_grid=phi_grid)
phi_wavefunc.amplitudes = standardize_sign(phi_wavefunc.amplitudes)
phi_wavefunc.amplitudes = amplitude_modifier(
phi_wavefunc.amplitudes)
wavefunctions.append(phi_wavefunc)
fig_ax = kwargs.get("fig_ax") or plt.subplots()
kwargs["fig_ax"] = fig_ax
kwargs = {
**self.wavefunction1d_defaults(mode,
evals,
wavefunc_count=len(wavefunc_indices)),
**kwargs,
}
# in merging the dictionaries in the previous line: if any duplicates,
# later ones survive
plot.wavefunction1d(
wavefunctions,
potential_vals=potential_vals,
offset=energies,
scaling=scaling,
**kwargs,
)
return fig_ax