Cos2PhiQubit¶

class scqubits.core.cos2phi_qubit.Cos2PhiQubit(EJ, ECJ, EL, EC, dL, dCJ, dEJ, flux, ng, ncut, zeta_cut, phi_cut, truncated_dim=6, id_str=None, evals_method=None, evals_method_options=None, esys_method=None, esys_method_options=None)[source]¶

Cosine Two Phi Qubit

[1] Smith et al., NPJ Quantum Inf. 6, 8 (2020) http://www.nature.com/articles/s41534-019-0231-2

\[\begin{split}H = & \,2 E_\text{CJ}'n_\phi^2 + 2 E_\text{CJ}' (n_\theta - n_\text{g} - n_\zeta)^2 + 4 E_\text{C} n_\zeta^2\\ & + E_\text{L}'(\phi - \pi\Phi_\text{ext}/\Phi_0)^2 + E_\text{L}' \zeta^2 - 2 E_\text{J}\cos{\theta}\cos{\phi} \\ & + 2 dE_\text{J} E_\text{J}\sin{\theta}\sin{\phi} \\ & - 4 dC_\text{J} E_\text{CJ}' n_\phi (n_\theta - n_\text{g}-n_\zeta) \\ & + dL E_\text{L}'(2\phi - \varphi_\text{ext})\zeta ,\end{split}\]

where \(E_\text{CJ}' = E_\text{CJ} / (1 - dC_\text{J})^2\) and \(E_\text{L}' = E_\text{L} / (1 - dL)^2\).

Parameters:

EJ (float) – Josephson energy of the two junctions
ECJ (float) – charging energy of the two junctions
EL (float) – inductive energy of the two inductors
EC (float) – charging energy of the shunt capacitor
dCJ (float) – disorder in junction charging energy
dL (float) – disorder in inductive energy
dEJ (float) – disorder in junction energy
flux (float) – external magnetic flux in units of one flux quantum
ng (float) – offset charge
ncut (int) – cutoff in charge basis, -ncut <= \(n_\theta\) <= ncut
zeta_cut (int) – number of harmonic oscillator basis states for \(\zeta\) variable
phi_cut (int) – number of harmonic oscillator basis states for \(\phi\) variable
truncated_dim (int) – desired dimension of the truncated quantum system; expected: truncated_dim > 1
id_str (Optional[str]) – optional string by which this instance can be referred to in HilbertSpace and ParameterSweep. If not provided, an id is auto-generated.
esys_method (Union[Callable, str, None]) – method for esys diagonalization, callable or string representation
esys_method_options (Optional[dict]) – dictionary with esys diagonalization options
evals_method (Union[Callable, str, None]) – method for evals diagonalization, callable or string representation
evals_method_options (Optional[dict]) – dictionary with evals diagonalization options

Methods

`Cos2PhiQubit.E01`()	Returns the qubit's fundamental energy splitting, E_1 - E_0.
`Cos2PhiQubit.__init__`(EJ, ECJ, EL, EC, dL, ...)
`Cos2PhiQubit.anharmonicity`()	Returns the qubit's anharmonicity, (E_2 - E_1) - (E_1 - E_0).
`Cos2PhiQubit.broadcast`(event, **kwargs)	Request a broadcast from CENTRAL_DISPATCH reporting event.
`Cos2PhiQubit.create`()	Use ipywidgets to create a new class instance
`Cos2PhiQubit.create_from_file`(filename)	Read initdata and spectral data from file, and use those to create a new SpectrumData object.
`Cos2PhiQubit.d_hamiltonian_d_EJ`([energy_esys])	Returns operator representing a derivative of the Hamiltonian with respect to EJ in the native or eigenenergy basis.
`Cos2PhiQubit.d_hamiltonian_d_flux`([energy_esys])	Returns operator representing a derivative of the Hamiltonian with respect to flux in the native or eigenenergy basis.
`Cos2PhiQubit.d_hamiltonian_d_ng`([energy_esys])	Returns operator representing a derivative of the Hamiltonian with respect to ng in the native or eigenenergy basis.
`Cos2PhiQubit.default_params`()	Return dictionary with default parameter values for initialization of class instance
`Cos2PhiQubit.deserialize`(io_data)	Take the given IOData and return an instance of the described class, initialized with the data stored in io_data.
`Cos2PhiQubit.effective_noise_channels`()	Return a list of noise channels that are used when calculating the effective noise (i.e. via t1_effective and t2_effective.
`Cos2PhiQubit.eigensys`([evals_count, ...])	Calculates eigenvalues and corresponding eigenvectors using scipy.linalg.eigh.
`Cos2PhiQubit.eigenvals`([evals_count, ...])	Calculates eigenvalues using scipy.linalg.eigh, returns numpy array of eigenvalues.
`Cos2PhiQubit.filewrite`(filename)	Convenience method bound to the class.
`Cos2PhiQubit.get_dispersion_vs_paramvals`(...)	Calculates eigenvalues/eigenstates for a varying system parameter, given an array of parameter values.
`Cos2PhiQubit.get_initdata`()	Returns dict appropriate for creating/initializing a new Serializable object.
`Cos2PhiQubit.get_matelements_vs_paramvals`(...)	Calculates matrix elements for a varying system parameter, given an array of parameter values.
`Cos2PhiQubit.get_operator_names`()	Returns a list of all operator names for the quantum system.
`Cos2PhiQubit.get_spectrum_vs_paramvals`(...)	Calculates eigenvalues/eigenstates for a varying system parameter, given an array of parameter values.
`Cos2PhiQubit.hamiltonian`([energy_esys])	Returns Hamiltonian in basis obtained by employing harmonic basis for \(\phi, \zeta\) and charge basis for \(\theta\) or in the eigenenerg basis.
`Cos2PhiQubit.hilbertdim`()	Returns total Hilbert space dimension
`Cos2PhiQubit.matrixelement_table`(operator[, ...])	Returns table of matrix elements for operator with respect to the eigenstates of the qubit.
`Cos2PhiQubit.n_1_operator`([energy_esys])	Returns operator representing the charge difference across junction 1 in native or eigenenergy basis.
`Cos2PhiQubit.n_2_operator`([energy_esys])	Returns operator representing the charge difference across junction 2 in native or eigenenergy basis.
`Cos2PhiQubit.n_phi_operator`([energy_esys])	Returns the \(n_\phi\) operator in the harmonic oscillator or eigenenergy basis.
`Cos2PhiQubit.n_theta_operator`([energy_esys])	Returns the \(n_\theta\) operator in the charge or eigenenergy basis.
`Cos2PhiQubit.n_zeta_operator`([energy_esys])	Returns the \(n_\zeta\) operator in the harmonic oscillator or eigenenergy basis.
`Cos2PhiQubit.phi_1_operator`([energy_esys])	Returns operator representing the phase across inductor 1 in harmonic oscillator or eigenenergy basis.
`Cos2PhiQubit.phi_2_operator`([energy_esys])	Returns operator representing the phase across inductor 2 in harmonic oscillator or eigenenergy basis.
`Cos2PhiQubit.phi_operator`([energy_esys])	Returns the \(\phi\) operator in the native or eigenenergy basis.
`Cos2PhiQubit.phi_osc`()	Returns oscillator strength of \(\phi\) degree of freedom
`Cos2PhiQubit.phi_plasma`()	Returns plasma oscillation frequency of \(\phi\) degree of freedom
`Cos2PhiQubit.plot_coherence_vs_paramvals`(...)	Show plots of coherence for various channels supported by the qubit as they vary as a function of a changing parameter.
`Cos2PhiQubit.plot_dispersion_vs_paramvals`(...)	Generates a simple plot of a set of curves representing the charge or flux dispersion of transition energies.
`Cos2PhiQubit.plot_evals_vs_paramvals`(...[, ...])	Generates a simple plot of a set of eigenvalues as a function of one parameter.
`Cos2PhiQubit.plot_matelem_vs_paramvals`(...)	Generates a simple plot of a set of eigenvalues as a function of one parameter.
`Cos2PhiQubit.plot_matrixelements`(operator[, ...])	Plots matrix elements for operator, given as a string referring to a class method that returns an operator matrix.
`Cos2PhiQubit.plot_potential`([phi_grid, ...])	Draw contour plot of the potential energy in \(\theta, \phi\) basis, at \(\zeta = 0\)
`Cos2PhiQubit.plot_t1_effective_vs_paramvals`(...)	Plot effective \(T_1\) coherence time (rate) as a function of changing parameter.
`Cos2PhiQubit.plot_t2_effective_vs_paramvals`(...)	Plot effective \(T_2\) coherence time (rate) as a function of changing parameter.
`Cos2PhiQubit.plot_wavefunction`([esys, ...])	Plots a 2D wave function in \(\theta, \phi\) basis, at \(\zeta = 0\)
`Cos2PhiQubit.potential`(phi, zeta, theta)	Returns full potential evaluated at \(\phi, \zeta, \theta\)
`Cos2PhiQubit.process_hamiltonian`(...[, ...])	Return qubit Hamiltonian in chosen basis: either return unchanged (i.e., in native basis) or transform into eigenenergy basis
`Cos2PhiQubit.process_op`(native_op[, energy_esys])	Processes the operator native_op: either hand back native_op unchanged, or transform it into the energy eigenbasis.
`Cos2PhiQubit.receive`(event, sender, **kwargs)	Receive a message from CENTRAL_DISPATCH and initiate action on it.
`Cos2PhiQubit.reduced_potential`(phi, theta)	Returns reduced potential by setting \(zeta = 0\)
`Cos2PhiQubit.serialize`()	Convert the content of the current class instance into IOData format.
`Cos2PhiQubit.set_and_return`(attr_name, value)	Allows to set an attribute after which self is returned. This is useful for doing something like example::.
`Cos2PhiQubit.set_params`(**kwargs)	Set new parameters through the provided dictionary.
`Cos2PhiQubit.set_params_from_gui`(change)	Set new parameters through the provided dictionary.
`Cos2PhiQubit.supported_noise_channels`()	Return a list of supported noise channels
`Cos2PhiQubit.t1`(i, j, noise_op, spectral_density)	Calculate the transition time (or rate) using Fermi's Golden Rule due to a noise channel with a spectral density spectral_density and system noise operator noise_op.
`Cos2PhiQubit.t1_capacitive`([i, j, Q_cap, T, ...])	\(T_1\) due to dielectric dissipation in the Josephson junction capacitances.
`Cos2PhiQubit.t1_charge_impedance`([i, j, Z, ...])	Noise due to charge coupling to an impedance (such as a transmission line).
`Cos2PhiQubit.t1_effective`([noise_channels, ...])	Calculate the effective \(T_1\) time (or rate).
`Cos2PhiQubit.t1_flux_bias_line`([i, j, M, Z, ...])	Noise due to a bias flux line.
`Cos2PhiQubit.t1_inductive`([i, j, Q_ind, T, ...])	\(T_1\) due to inductive dissipation in superinductors.
`Cos2PhiQubit.t1_purcell`([i, j, Q_cap, T, ...])	\(T_1\) due to dielectric dissipation in the shunt capacitor.
`Cos2PhiQubit.t1_quasiparticle_tunneling`([i, ...])	Noise due to quasiparticle tunneling across a Josephson junction.
`Cos2PhiQubit.t2_effective`([noise_channels, ...])	Calculate the effective \(T_2\) time (or rate).
`Cos2PhiQubit.total_identity`()	Returns Identity operator acting on the total Hilbert space.
`Cos2PhiQubit.tphi_1_over_f`(A_noise, i, j, ...)	Calculate the 1/f dephasing time (or rate) due to arbitrary noise source.
`Cos2PhiQubit.tphi_1_over_f_cc`([A_noise, i, ...])	Calculate the 1/f dephasing time (or rate) due to critical current noise.
`Cos2PhiQubit.tphi_1_over_f_flux`([A_noise, ...])	Calculate the 1/f dephasing time (or rate) due to flux noise.
`Cos2PhiQubit.tphi_1_over_f_ng`([A_noise, i, ...])	Calculate the 1/f dephasing time (or rate) due to charge noise.
`Cos2PhiQubit.wavefunction`([esys, which, ...])	Return a 3D wave function in \(\phi, \zeta, \theta\) basis
`Cos2PhiQubit.widget`([params])	Use ipywidgets to modify parameters of class instance
`Cos2PhiQubit.zeta_operator`([energy_esys])	Returns the \(\zeta\) operator in the harmonic oscillator or eigenenergy basis.
`Cos2PhiQubit.zeta_osc`()	Returns oscillator strength of \(\zeta\) degree of freedom
`Cos2PhiQubit.zeta_plasma`()	Returns plasma oscillation frequency of \(\zeta\) degree of freedom

Attributes

`EC`	Descriptor class for properties that are to be monitored for changes.
`ECJ`	Descriptor class for properties that are to be monitored for changes.
`EJ`	Descriptor class for properties that are to be monitored for changes.
`EL`	Descriptor class for properties that are to be monitored for changes.
`dCJ`	Descriptor class for properties that are to be monitored for changes.
`dEJ`	Descriptor class for properties that are to be monitored for changes.
`dL`	Descriptor class for properties that are to be monitored for changes.
`flux`	Descriptor class for properties that are to be monitored for changes.
`id_str`
`ncut`	Descriptor class for properties that are to be monitored for changes.
`ng`	Descriptor class for properties that are to be monitored for changes.
`phi_cut`	Descriptor class for properties that are to be monitored for changes.
`truncated_dim`	Descriptor class for properties that are to be monitored for changes.
`zeta_cut`	Descriptor class for properties that are to be monitored for changes.

E01()¶

Returns the qubit’s fundamental energy splitting, E_1 - E_0.

Return type:: float

anharmonicity()¶

Returns the qubit’s anharmonicity, (E_2 - E_1) - (E_1 - E_0).

Return type:: float

broadcast(event, **kwargs)¶

Request a broadcast from CENTRAL_DISPATCH reporting event.

Parameters:

event (str) – event name from EVENTS
**kwargs

Return type:

None

classmethod create()[source]¶

Use ipywidgets to create a new class instance

Return type:: Cos2PhiQubit

classmethod create_from_file(filename)¶

Read initdata and spectral data from file, and use those to create a new SpectrumData object.

Returns:: new SpectrumData object, initialized with data read from file
Return type:: SpectrumData
Parameters:: filename (str)

d_hamiltonian_d_EJ(energy_esys=False)[source]¶

Returns operator representing a derivative of the Hamiltonian with respect to EJ in the native or eigenenergy basis.

Parameters:: energy_esys (Union[bool, Tuple[ndarray, ndarray]]) – If False (default), returns operator in the native basis. If True, the energy eigenspectrum is computed, returns operator in the energy eigenbasis. If energy_esys = esys, where esys is a tuple containing two ndarrays (eigenvalues and energy eigenvectors), returns operator in the energy eigenbasis, and does not have to recalculate eigenspectrum.
Return type:: Union[ndarray, csc_matrix]
Returns:: Operator in chosen basis. If native basis chosen, operator returned as a csc_matrix. If the eigenenergy basis is chosen, unless energy_esys is specified, operator has dimensions of truncated_dim x truncated_dim, and is returned as an ndarray. Otherwise, if eigenenergy basis is chosen, operator has dimensions of m x m, for m given eigenvectors, and is returned as an ndarray.

d_hamiltonian_d_flux(energy_esys=False)[source]¶

Returns operator representing a derivative of the Hamiltonian with respect to flux in the native or eigenenergy basis.

Parameters:: energy_esys (Union[bool, Tuple[ndarray, ndarray]]) – If False (default), returns operator in the native basis. If True, the energy eigenspectrum is computed, returns operator in the energy eigenbasis. If energy_esys = esys, where esys is a tuple containing two ndarrays (eigenvalues and energy eigenvectors), returns operator in the energy eigenbasis, and does not have to recalculate eigenspectrum.
Return type:: Union[ndarray, csc_matrix]
Returns:: Operator in chosen basis. If native basis chosen, operator returned as a csc_matrix. If the eigenenergy basis is chosen, unless energy_esys is specified, operator has dimensions of truncated_dim x truncated_dim, and is returned as an ndarray. Otherwise, if eigenenergy basis is chosen, operator has dimensions of m x m, for m given eigenvectors, and is returned as an ndarray.

d_hamiltonian_d_ng(energy_esys=False)[source]¶

Returns operator representing a derivative of the Hamiltonian with respect to ng in the native or eigenenergy basis.

Parameters:: energy_esys (Union[bool, Tuple[ndarray, ndarray]]) – If False (default), returns operator in the native basis. If True, the energy eigenspectrum is computed, returns operator in the energy eigenbasis. If energy_esys = esys, where esys is a tuple containing two ndarrays (eigenvalues and energy eigenvectors), returns operator in the energy eigenbasis, and does not have to recalculate eigenspectrum.
Return type:: Union[ndarray, csc_matrix]
Returns:: Operator in chosen basis. If native basis chosen, operator returned as a csc_matrix. If the eigenenergy basis is chosen, unless energy_esys is specified, operator has dimensions of truncated_dim x truncated_dim, and is returned as an ndarray. Otherwise, if eigenenergy basis is chosen, operator has dimensions of m x m, for m given eigenvectors, and is returned as an ndarray.

static default_params()[source]¶

Return dictionary with default parameter values for initialization of class instance

Return type:: Dict[str, Any]

classmethod deserialize(io_data)¶

Take the given IOData and return an instance of the described class, initialized with the data stored in io_data.

Return type:: TypeVar(SerializableType, bound= Serializable)
Parameters:: io_data (IOData)

classmethod effective_noise_channels()¶

Return a list of noise channels that are used when calculating the effective noise (i.e. via t1_effective and t2_effective.

Return type:: List[str]

eigensys(evals_count=6, filename=None, return_spectrumdata=False)¶

Calculates eigenvalues and corresponding eigenvectors using scipy.linalg.eigh. Returns two numpy arrays containing the eigenvalues and eigenvectors, respectively.

Parameters:

evals_count (int) – number of desired eigenvalues/eigenstates (default value = 6)
filename (Optional[str]) – path and filename without suffix, if file output desired (default value = None)
return_spectrumdata (if set to true, the returned data is provided as a SpectrumData object) – (default value = False)

Return type:

Union[Tuple[ndarray, ndarray], SpectrumData]

Returns:

eigenvalues, eigenvectors as numpy arrays or in form of a SpectrumData object

eigenvals(evals_count=6, filename=None, return_spectrumdata=False)¶

Calculates eigenvalues using scipy.linalg.eigh, returns numpy array of eigenvalues.

Parameters:

evals_count (int) – number of desired eigenvalues/eigenstates (default value = 6)
filename (Optional[str]) – path and filename without suffix, if file output desired (default value = None)
return_spectrumdata (bool) – if set to true, the returned data is provided as a SpectrumData object (default value = False)

Return type:

Union[SpectrumData, ndarray]

Returns:

eigenvalues as ndarray or in form of a SpectrumData object

filewrite(filename)¶

Convenience method bound to the class. Simply accesses the write function.

Return type:: None
Parameters:: filename (str)

get_dispersion_vs_paramvals(dispersion_name, param_name, param_vals, ref_param=None, transitions=(0, 1), levels=None, point_count=50, num_cpus=None)¶

Calculates eigenvalues/eigenstates for a varying system parameter, given an array of parameter values. Returns a SpectrumData object with energy_data[n] containing eigenvalues calculated for parameter value param_vals[n].

Parameters:

dispersion_name (str) – parameter inducing the dispersion, typically ‘ng’ or ‘flux’ (will be scanned over range from 0 to 1)
param_name (str) – name of parameter to be varied
param_vals (ndarray) – parameter values to be plugged in
ref_param (Optional[str]) – optional, name of parameter to use as reference for the parameter value; e.g., to compute charge dispersion vs. EJ/EC, use EJ as param_name and EC as ref_param
transitions (Union[Tuple[int, int], Tuple[Tuple[int, int], ...]]) – integer tuple or tuples specifying for which transitions dispersion is to be calculated (default: = (0,1))
levels (Union[int, Tuple[int, ...], None]) – tuple specifying levels (rather than transitions) for which dispersion should be plotted; overrides transitions parameter when given
point_count (int) – number of points scanned for the dispersion parameter for determining min and max values of transition energies (default: 50)
num_cpus (Optional[int]) – number of cores to be used for computation (default value: settings.NUM_CPUS)

Return type:

SpectrumData

get_initdata()¶

Returns dict appropriate for creating/initializing a new Serializable object.

Return type:: Dict[str, Any]

get_matelements_vs_paramvals(operator, param_name, param_vals, evals_count=6, num_cpus=None)¶

Calculates matrix elements for a varying system parameter, given an array of parameter values. Returns a SpectrumData object containing matrix element data, eigenvalue data, and eigenstate data..

Parameters:

operator (str) – name of class method in string form, returning operator matrix
param_name (str) – name of parameter to be varied
param_vals (ndarray) – parameter values to be plugged in
evals_count (int) – number of desired eigenvalues (sorted from smallest to largest) (default value = 6)
num_cpus (Optional[int]) – number of cores to be used for computation (default value: settings.NUM_CPUS)

Return type:

SpectrumData

classmethod get_operator_names()¶

Returns a list of all operator names for the quantum system. Note that this list omits any operators that start with “_”.

Parameters:: subsys – Class instance of quantum system
Return type:: List[str]
Returns:: list of operator names

get_spectrum_vs_paramvals(param_name, param_vals, evals_count=6, subtract_ground=False, get_eigenstates=False, filename=None, num_cpus=None)¶

Parameters:

param_name (str) – name of parameter to be varied
param_vals (ndarray) – parameter values to be plugged in
evals_count (int) – number of desired eigenvalues (sorted from smallest to largest) (default value = 6)
subtract_ground (bool) – if True, eigenvalues are returned relative to the ground state eigenvalue (default value = False)
get_eigenstates (bool) – return eigenstates along with eigenvalues (default value = False)
filename (str) – file name if direct output to disk is wanted
num_cpus (Optional[int]) – number of cores to be used for computation (default value: settings.NUM_CPUS)

Return type:

SpectrumData

hamiltonian(energy_esys=False)[source]¶

Returns Hamiltonian in basis obtained by employing harmonic basis for \(\phi, \zeta\) and charge basis for \(\theta\) or in the eigenenerg basis.

Parameters:: energy_esys (Union[bool, Tuple[ndarray, ndarray]]) – If False (default), returns Hamiltonian in basis obtained by employing harmonic basis for \(\phi, \zeta\) and charge basis for \(\theta\). If True, the energy eigenspectrum is computed, returns Hamiltonian in the energy eigenbasis. If energy_esys = esys, where esys is a tuple containing two ndarrays (eigenvalues and energy eigenvectors), returns Hamiltonian in the energy eigenbasis, and does not have to recalculate eigenspectrum.
Return type:: csc_matrix
Returns:: Hamiltonian in chosen basis as csc_matrix. If the eigenenergy basis is chosen, unless energy_esys is specified, the Hamiltonian has dimensions of truncated_dim x truncated_dim. Otherwise, if eigenenergy basis is chosen, Hamiltonian has dimensions of m x m, for m given eigenvectors.

hilbertdim()[source]¶

Returns total Hilbert space dimension

Return type:: int

matrixelement_table(operator, evecs=None, evals_count=6, filename=None, return_datastore=False)¶

Returns table of matrix elements for operator with respect to the eigenstates of the qubit. The operator is given as a string matching a class method returning an operator matrix. E.g., for an instance trm of Transmon, the matrix element table for the charge operator is given by trm.op_matrixelement_table(‘n_operator’). When esys is set to None, the eigensystem is calculated on-the-fly.

Parameters:

operator (str) – name of class method in string form, returning operator matrix in qubit-internal basis.
evecs (ndarray) – if not provided, then the necessary eigenstates are calculated on the fly
evals_count (int) – number of desired matrix elements, starting with ground state (default value = 6)
filename (str) – output file name
return_datastore (bool) – if set to true, the returned data is provided as a DataStore object (default value = False)

Return type:

Union[DataStore, ndarray]

n_1_operator(energy_esys=False)[source]¶

Returns operator representing the charge difference across junction 1 in native or eigenenergy basis.

Parameters:: energy_esys (Union[bool, Tuple[ndarray, ndarray]]) – If False (default), returns operator in the harmonic oscillator basis. If True, the energy eigenspectrum is computed, returns operator in the energy eigenbasis. If energy_esys = esys, where esys is a tuple containing two ndarrays (eigenvalues and energy eigenvectors), returns operator in the energy eigenbasis, and does not have to recalculate eigenspectrum.
Return type:: Union[ndarray, csc_matrix]
Returns:: Operator in chosen basis. If native basis chosen, operator returned as a csc_matrix. If the eigenenergy basis is chosen, unless energy_esys is specified, operator has dimensions of truncated_dim x truncated_dim, and is returned as an ndarray. Otherwise, if eigenenergy basis is chosen, operator has dimensions of m x m, for m given eigenvectors, and is returned as an ndarray.

n_2_operator(energy_esys=False)[source]¶

Returns operator representing the charge difference across junction 2 in native or eigenenergy basis.

Parameters:: energy_esys (Union[bool, Tuple[ndarray, ndarray]]) – If False (default), returns operator in the harmonic oscillator basis. If True, the energy eigenspectrum is computed, returns operator in the energy eigenbasis. If energy_esys = esys, where esys is a tuple containing two ndarrays (eigenvalues and energy eigenvectors), returns operator in the energy eigenbasis, and does not have to recalculate eigenspectrum.
Return type:: Union[ndarray, csc_matrix]
Returns:: Operator in chosen basis. If native basis chosen, operator returned as a csc_matrix. If the eigenenergy basis is chosen, unless energy_esys is specified, operator has dimensions of truncated_dim x truncated_dim, and is returned as an ndarray. Otherwise, if eigenenergy basis is chosen, operator has dimensions of m x m, for m given eigenvectors, and is returned as an ndarray.

n_phi_operator(energy_esys=False)[source]¶

Returns the \(n_\phi\) operator in the harmonic oscillator or eigenenergy basis.

Parameters:: energy_esys (Union[bool, Tuple[ndarray, ndarray]]) – If False (default), returns \(n_\phi\) operator in the native basis. If True, the energy eigenspectrum is computed, returns \(n_\phi\) operator in the energy eigenbasis. If energy_esys = esys, where esys is a tuple containing two ndarrays (eigenvalues and energy eigenvectors), returns \(n_\phi\) operator in the energy eigenbasis, and does not have to recalculate eigenspectrum.
Return type:: Union[ndarray, coo_matrix]
Returns:: \(n_\phi\) operator in chosen basis. If native basis chosen, operator returned as a csc_matrix. If the eigenenergy basis is chosen, unless energy_esys is specified, \(n_\phi\) operator has dimensions of truncated_dim x truncated_dim, and is returned as an ndarray. Otherwise, if eigenenergy basis is chosen, \(n_\phi\) operator has dimensions of m x m, for m given eigenvectors, and is returned as an ndarray \(\zeta\).

n_theta_operator(energy_esys=False)[source]¶

Returns the \(n_\theta\) operator in the charge or eigenenergy basis.

Parameters:: energy_esys (Union[bool, Tuple[ndarray, ndarray]]) – If False (default), returns \(n_\theta\) operator in the charge basis. If True, the energy eigenspectrum is computed, returns \(n_\theta\) operator in the energy eigenbasis. If energy_esys = esys, where esys is a tuple containing two ndarrays (eigenvalues and energy eigenvectors), returns \(n_\theta\) operator in the energy eigenbasis, and does not have to recalculate eigenspectrum.
Return type:: Union[ndarray, csc_matrix]
Returns:: \(n_\theta\) operator in chosen basis. If charge basis chosen, operator returned as a csc_matrix. If the eigenenergy basis is chosen, unless energy_esys is specified, \(n_\theta\) operator has dimensions of truncated_dim x truncated_dim, and is returned as an ndarray. Otherwise, if eigenenergy basis is chosen, \(n_\theta\) operator has dimensions of m x m, for m given eigenvectors, and is returned as an ndarray.

n_zeta_operator(energy_esys=False)[source]¶

Returns the \(n_\zeta\) operator in the harmonic oscillator or eigenenergy basis.

Parameters:: energy_esys (Union[bool, Tuple[ndarray, ndarray]]) – If False (default), returns \(n_\zeta\) operator in the native basis. If True, the energy eigenspectrum is computed, returns \(n_\zeta\) operator in the energy eigenbasis. If energy_esys = esys, where esys is a tuple containing two ndarrays (eigenvalues and energy eigenvectors), returns \(n_\zeta\) operator in the energy eigenbasis, and does not have to recalculate eigenspectrum.
Return type:: Union[ndarray, csc_matrix]
Returns:: \(n_\zeta\) operator in chosen basis. If native basis chosen, operator returned as a csc_matrix. If the eigenenergy basis is chosen, unless energy_esys is specified, \(n_\zeta\) operator has dimensions of truncated_dim x truncated_dim, and is returned as an ndarray. Otherwise, if eigenenergy basis is chosen, \(n_\zeta\) operator has dimensions of m x m, for m given eigenvectors, and is returned as an ndarray.

phi_1_operator(energy_esys=False)[source]¶

Returns operator representing the phase across inductor 1 in harmonic oscillator or eigenenergy basis.

Parameters:: energy_esys (Union[bool, Tuple[ndarray, ndarray]]) – If False (default), returns operator in the harmonic oscillator basis. If True, the energy eigenspectrum is computed, returns operator in the energy eigenbasis. If energy_esys = esys, where esys is a tuple containing two ndarrays (eigenvalues and energy eigenvectors), returns operator in the energy eigenbasis, and does not have to recalculate eigenspectrum.
Return type:: Union[ndarray, csc_matrix]
Returns:: Operator in chosen basis. If harmonic oscillator basis chosen, operator returned as a csc_matrix. If the eigenenergy basis is chosen, unless energy_esys is specified, operator has dimensions of truncated_dim x truncated_dim, and is returned as an ndarray. Otherwise, if eigenenergy basis is chosen, operator has dimensions of m x m, for m given eigenvectors, and is returned as an ndarray.

phi_2_operator(energy_esys=False)[source]¶

Returns operator representing the phase across inductor 2 in harmonic oscillator or eigenenergy basis.

Parameters:: energy_esys (Union[bool, Tuple[ndarray, ndarray]]) – If False (default), returns operator in the harmonic oscillator basis. If True, the energy eigenspectrum is computed, returns operator in the energy eigenbasis. If energy_esys = esys, where esys is a tuple containing two ndarrays (eigenvalues and energy eigenvectors), returns operator in the energy eigenbasis, and does not have to recalculate eigenspectrum.
Return type:: Union[ndarray, csc_matrix]
Returns:: Operator in chosen basis. If harmonic oscillator basis chosen, operator returned as a csc_matrix. If the eigenenergy basis is chosen, unless energy_esys is specified, operator has dimensions of truncated_dim x truncated_dim, and is returned as an ndarray. Otherwise, if eigenenergy basis is chosen, operator has dimensions of m x m, for m given eigenvectors, and is returned as an ndarray.

phi_operator(energy_esys=False)[source]¶

Returns the \(\phi\) operator in the native or eigenenergy basis.

Parameters:: energy_esys (Union[bool, Tuple[ndarray, ndarray]]) – If False (default), returns \(\phi\) operator in the native basis. If True, the energy eigenspectrum is computed, returns \(\phi\) operator in the energy eigenbasis. If energy_esys = esys, where esys is a tuple containing two ndarrays (eigenvalues and energy eigenvectors), returns \(\phi\) operator in the energy eigenbasis, and does not have to recalculate eigenspectrum.
Return type:: Union[ndarray, csc_matrix]
Returns:: \(\phi\) operator in chosen basis. If native basis chosen, operator returned as a csc_matrix. If the eigenenergy basis is chosen, unless energy_esys is specified, \(\phi\) operator has dimensions of truncated_dim x truncated_dim, and is returned as an ndarray. Otherwise, if eigenenergy basis is chosen, \(\phi\) operator has dimensions of m x m, for m given eigenvectors, and is returned as an ndarray.

phi_osc()[source]¶

Returns oscillator strength of \(\phi\) degree of freedom

Return type:: float

phi_plasma()[source]¶

Returns plasma oscillation frequency of \(\phi\) degree of freedom

Return type:: float

plot_coherence_vs_paramvals(param_name, param_vals, noise_channels=None, common_noise_options=None, spectrum_data=None, scale=1, num_cpus=None, **kwargs)¶

Show plots of coherence for various channels supported by the qubit as they vary as a function of a changing parameter.

For example, assuming qubit is a qubit object with flux being one of its parameters, one can see how coherence due to various noise channels vary as the flux changes:

qubit.plot_coherence_vs_paramvals(param_name='flux',
                                  param_vals=np.linspace(-0.5, 0.5, 100),
                                  scale=1e-3,
                                  ylabel=r"$\mu s$");

Parameters:

param_name (str) – name of parameter to be varied
param_vals (ndarray) – parameter values to be plugged in
noise_channels (Union[str, List[str], List[Tuple[str, Dict]]]) – channels to be plotted, if None then noise channels given by supported_noise_channels are used
common_noise_options (Dict) – common options used when calculating coherence times
spectrum_data (SpectrumData) – spectral data used during noise calculations
scale (float) – a number that all data is multiplied by before being plotted
num_cpus (Optional[int]) – number of cores to be used for computation

Return type:

Figure, Axes

plot_dispersion_vs_paramvals(dispersion_name, param_name, param_vals, ref_param=None, transitions=(0, 1), levels=None, point_count=50, num_cpus=None, **kwargs)¶

Generates a simple plot of a set of curves representing the charge or flux dispersion of transition energies.

Parameters:

dispersion_name (str) – parameter inducing the dispersion, typically ‘ng’ or ‘flux’ (will be scanned over range from 0 to 1)
param_name (str) – name of parameter to be varied
param_vals (ndarray) – parameter values to be plugged in
ref_param (Optional[str]) – optional, name of parameter to use as reference for the parameter value; e.g., to compute charge dispersion vs. EJ/EC, use EJ as param_name and EC as ref_param
transitions (Union[Tuple[int, int], Tuple[Tuple[int, int], ...]]) – integer tuple or tuples specifying for which transitions dispersion is to be calculated (default: = (0,1))
levels (Union[int, Tuple[int, ...], None]) – int or tuple specifying level(s) (rather than transitions) for which dispersion should be plotted; overrides transitions parameter when given
point_count (int) – number of points scanned for the dispersion parameter for determining min and max values of transition energies (default: 50)
num_cpus (Optional[int]) – number of cores to be used for computation (default value: settings.NUM_CPUS)
**kwargs – standard plotting option (see separate documentation)

Return type:

Tuple[Figure, Axes]

plot_evals_vs_paramvals(param_name, param_vals, evals_count=6, subtract_ground=False, num_cpus=None, **kwargs)¶

Generates a simple plot of a set of eigenvalues as a function of one parameter. The individual points correspond to the a provided array of parameter values.

Parameters:

param_name (str) – name of parameter to be varied
param_vals (ndarray) – parameter values to be plugged in
evals_count (int) – number of desired eigenvalues (sorted from smallest to largest) (default value = 6)
subtract_ground (bool) – whether to subtract ground state energy from all eigenvalues (default value = False)
num_cpus (Optional[int]) – number of cores to be used for computation (default value: settings.NUM_CPUS)
**kwargs – standard plotting option (see separate documentation)

Return type:

Tuple[Figure, Axes]

plot_matelem_vs_paramvals(operator, param_name, param_vals, select_elems=4, mode='abs', num_cpus=None, **kwargs)¶

Generates a simple plot of a set of eigenvalues as a function of one parameter. The individual points correspond to the a provided array of parameter values.

Parameters:

operator (str) – name of class method in string form, returning operator matrix
param_name (str) – name of parameter to be varied
param_vals (ndarray) – parameter values to be plugged in
select_elems (Union[int, List[Tuple[int, int]]]) – either maximum index of desired matrix elements, or list [(i1, i2), (i3, i4), …] of index tuples for specific desired matrix elements (default value = 4)
mode (str) – idx_entry from MODE_FUNC_DICTIONARY, e.g., ‘abs’ for absolute value (default value = ‘abs’)
num_cpus (Optional[int]) – number of cores to be used for computation (default value: settings.NUM_CPUS)
**kwargs – standard plotting option (see separate documentation)

Return type:

Tuple[Figure, Axes]

plot_matrixelements(operator, evecs=None, evals_count=6, mode='abs', show_numbers=False, show3d=True, **kwargs)¶

Plots matrix elements for operator, given as a string referring to a class method that returns an operator matrix. E.g., for instance trm of Transmon, the matrix element plot for the charge operator n is obtained by trm.plot_matrixelements(‘n’). When esys is set to None, the eigensystem with which eigenvectors is calculated.

Parameters:

operator (str) – name of class method in string form, returning operator matrix
evecs (ndarray) – eigensystem data of evals, evecs; eigensystem will be calculated if set to None (default value = None)
evals_count (int) – number of desired matrix elements, starting with ground state (default value = 6)
mode (str) – idx_entry from MODE_FUNC_DICTIONARY, e.g., ‘abs’ for absolute value (default)
show_numbers (bool) – determines whether matrix element values are printed on top of the plot (default: False)
show3d (bool) – whether to show a 3d skyscraper plot of the matrix alongside the 2d plot (default: True)
**kwargs – standard plotting option (see separate documentation)

Return type:

Union[Tuple[Figure, Tuple[Axes, Axes]], Tuple[Figure, Axes]]

plot_potential(phi_grid=None, theta_grid=None, contour_vals=None, **kwargs)[source]¶

Draw contour plot of the potential energy in \(\theta, \phi\) basis, at \(\zeta = 0\)

Parameters:

phi_grid (Grid1d, option) – used for setting a custom grid for phi; if None use self._default_phi_grid
theta_grid (Grid1d, option) – used for setting a custom grid for theta; if None use self._default_theta_grid
contour_vals (list, optional)
**kwargs – plotting parameters

Return type:

Tuple[Figure, Axes]

plot_t1_effective_vs_paramvals(param_name, param_vals, noise_channels=None, common_noise_options=None, spectrum_data=None, get_rate=False, scale=1, num_cpus=None, **kwargs)¶

Plot effective \(T_1\) coherence time (rate) as a function of changing parameter.

The effective \(T_1\) is calculated by considering a variety of depolarizing noise channels, according to the formula:

\[\frac{1}{T_{1}^{\rm eff}} = \frac{1}{2} \sum_k \frac{1}{T_{1}^{k}}\]

where \(k\) runs over the channels that can contribute to the effective noise. By default all the depolarizing noise channels given by the method effective_noise_channels are included.

For example, assuming qubit is a qubit object with flux being one of its parameters, one can see how the effective \(T_1\) varies as the flux changes:

qubit.plot_t1_effective_vs_paramvals(param_name='flux',
                                     param_vals=np.linspace(-0.5, 0.5, 100),
                                    );

Parameters:

param_name (str) – name of parameter to be varied
param_vals (ndarray) – parameter values to be plugged in
noise_channels (Union[str, List[str], List[Tuple[str, Dict]]]) – channels to be plotted, if None then noise channels given by supported_noise_channels are used
common_noise_options (Dict) – common options used when calculating coherence times
spectrum_data (SpectrumData) – spectral data used during noise calculations
get_rate (bool) – determines if rate or time should be plotted
scale (float) – a number that all data is multiplied by before being plotted
num_cpus (Optional[int]) – number of cores to be used for computation

Return type:

Figure, Axes

plot_t2_effective_vs_paramvals(param_name, param_vals, noise_channels=None, common_noise_options=None, spectrum_data=None, get_rate=False, scale=1, num_cpus=None, **kwargs)¶

Plot effective \(T_2\) coherence time (rate) as a function of changing parameter.

The effective \(T_2\) is calculated from both pure dephasing channels, as well as depolarization channels, according to the formula:

\[\frac{1}{T_{2}^{\rm eff}} = \sum_k \frac{1}{T_{\phi}^{k}} + \frac{1}{2} \sum_j \frac{1}{T_{1}^{j}}\]

where \(k\) (\(j\)) run over the relevant pure dephasing ( depolarization) channels that can contribute to the effective noise. By default all noise channels given by the method effective_noise_channels are included.

For example, assuming qubit is a qubit object with flux being one of its parameters, one can see how the effective \(T_2\) varies as the flux changes:

qubit.plot_t2_effective_vs_paramvals(param_name='flux',
                                     param_vals=np.linspace(-0.5, 0.5, 100),
                                    );

Parameters:

param_name (str) – name of parameter to be varied
param_vals (ndarray) – parameter values to be plugged in
noise_channels (Union[str, List[str], List[Tuple[str, Dict]]]) – channels to be plotted, if None then noise channels given by supported_noise_channels are used
common_noise_options (Dict) – common options used when calculating coherence times
spectrum_data (SpectrumData) – spectral data used during noise calculations
get_rate (bool) – determines if rate or time should be plotted
scale (float) – a number that all data is multiplied by before being plotted
num_cpus (Optional[int]) – number of cores to be used for computation

Return type:

Figure, Axes

plot_wavefunction(esys=None, which=0, phi_grid=None, theta_grid=None, mode='abs', zero_calibrate=True, **kwargs)[source]¶

Plots a 2D wave function in \(\theta, \phi\) basis, at \(\zeta = 0\)

Parameters:

esys (ndarray, ndarray) – eigenvalues, eigenvectors as obtained from .eigensystem()
which (int, optional) – index of wave function to be plotted (default value = (0)
phi_grid (Grid1d, option) – used for setting a custom grid for phi; if None use self._default_phi_grid
theta_grid (Grid1d, option) – used for setting a custom grid for theta; if None use self._default_theta_grid
mode (str, optional) – choices as specified in constants.MODE_FUNC_DICT (default value = ‘abs_sqr’)
zero_calibrate (bool, optional) – if True, colors are adjusted to use zero wavefunction amplitude as the neutral color in the palette
**kwargs – plot options

Return type:

Tuple[Figure, Axes]

potential(phi, zeta, theta)[source]¶

Returns full potential evaluated at \(\phi, \zeta, \theta\)

Parameters:

phi (float or ndarray) – float value of the phase variable phi
zeta (float or ndarray) – float value of the phase variable zeta
theta (float or ndarray) – float value of the phase variable theta

Return type:

float

process_hamiltonian(native_hamiltonian, energy_esys=False)¶

Return qubit Hamiltonian in chosen basis: either return unchanged (i.e., in native basis) or transform into eigenenergy basis

Parameters:

native_hamiltonian (Union[ndarray, csc_matrix]) – Hamiltonian in native basis
energy_esys (Union[bool, Tuple[ndarray, ndarray]]) – If False (default), returns Hamiltonian in the native basis If True, the energy eigenspectrum is computed, returns Hamiltonian in the energy eigenbasis if energy_esys is the energy eigenspectrum, in the form of a tuple containing two ndarrays (eigenvalues and energy eigenvectors), returns Hamiltonian in the energy eigenbasis, and does not have to recalculate eigenspectrum.

Return type:

Union[ndarray, csc_matrix]

Returns:

Hamiltonian, either unchanged in native basis, or transformed into eigenenergy basis

process_op(native_op, energy_esys=False)¶

Processes the operator native_op: either hand back native_op unchanged, or transform it into the energy eigenbasis. (Native basis refers to the basis used internally by each qubit, e.g., charge basis in the case of Transmon.

Parameters:

native_op (Union[ndarray, csc_matrix]) – operator in native basis
energy_esys (Union[bool, Tuple[ndarray, ndarray]]) – If False (default), returns operator in the native basis If True, the energy eigenspectrum is computed, returns operator in the energy eigenbasis if energy_esys is the energy eigenspectrum, in the form of a tuple containing two ndarrays (eigenvalues and energy eigenvectors), returns operator in the energy eigenbasis, and does not have to recalculate eigenspectrum.

Return type:

Union[ndarray, csc_matrix]

Returns:

native_op either unchanged or transformed into eigenenergy basis

receive(event, sender, **kwargs)¶

Receive a message from CENTRAL_DISPATCH and initiate action on it.

Parameters:

event (str) – event name from EVENTS
sender (DispatchClient) – original sender reporting the event
**kwargs

Return type:

None

reduced_potential(phi, theta)[source]¶

Returns reduced potential by setting \(zeta = 0\)

Return type:: float

serialize()¶

Convert the content of the current class instance into IOData format.

Return type:: IOData

set_and_return(attr_name, value)¶

Allows to set an attribute after which self is returned. This is useful for doing something like example:

qubit.set_and_return('flux', 0.23).some_method()

instead of example:

qubit.flux=0.23
qubit.some_method()

Parameters:

attr_name (str) – name of class attribute in string form
value (Any) – value that the attribute is to be set to

Return type:

QubitBaseClass

Returns:

self

set_params(**kwargs)¶: Set new parameters through the provided dictionary.

set_params_from_gui(change)¶: Set new parameters through the provided dictionary.

classmethod supported_noise_channels()[source]¶

Return a list of supported noise channels

Return type:: List[str]

t1(i, j, noise_op, spectral_density, T=0.015, total=True, esys=None, get_rate=False)¶

Calculate the transition time (or rate) using Fermi’s Golden Rule due to a noise channel with a spectral density spectral_density and system noise operator noise_op. Mathematically, it reads:

\[\frac{1}{T_1} = \frac{1}{\hbar^2} |\langle i| A_{\rm noise} | j \rangle|^2 S(\omega)\]

We assume that the qubit energies (or the passed in eigenspectrum) has units of frequency (and not angular frequency).

The spectral_density argument should be a callable object (typically a function) of one argument, which is assumed to be an angular frequency (in the units currently set as system units.

Parameters:

i (int >=0) – state index that along with j defines a transition (i->j)
j (int >=0) – state index that along with i defines a transition (i->j)
noise_op (Union[ndarray, csc_matrix]) – noise operator
T (float) – Temperature defined in Kelvin
spectral_density (Callable) – defines a spectral density, must take two arguments: omega and T (assumed to be in units of 2 pi * <system units>)
total (bool) – if False return a time/rate associated with a transition from state i to state j. if True return a time/rate associated with both i to j and j to i transitions
esys (Tuple[ndarray, ndarray]) – evals, evecs tuple
get_rate (bool) – get rate or time

Returns:

time or rate – decoherence time in units of \(2\pi ({\rm system\,\,units})\), or rate in inverse units.

Return type:

float

t1_capacitive(i=1, j=0, Q_cap=None, T=0.015, total=True, esys=None, get_rate=False)¶

\(T_1\) due to dielectric dissipation in the Josephson junction capacitances.

References: Nguyen et al (2019), Smith et al (2020)

Parameters:

i (int >=0) – state index that along with j defines a transition (i->j)
j (int >=0) – state index that along with i defines a transition (i->j)
Q_cap (Union[float, Callable]) – capacitive quality factor; a fixed value or function of omega
T (float) – temperature in Kelvin
total (bool) – if False return a time/rate associated with a transition from state i to state j. if True return a time/rate associated with both i to j and j to i transitions
esys (Tuple[ndarray, ndarray]) – evals, evecs tuple
get_rate (bool) – get rate or time

Returns:

time or rate –

decoherence time in units of \(2\pi ({\rm system\,\,units})\), or rate: in inverse units.

Return type:

float

t1_charge_impedance(i=1, j=0, Z=50, T=0.015, total=True, esys=None, get_rate=False, noise_op=None)¶

Noise due to charge coupling to an impedance (such as a transmission line).

References: Schoelkopf et al (2003), Ithier et al (2005)

Parameters:

i (int >=0) – state index that along with j defines a transition (i->j)
j (int >=0) – state index that along with i defines a transition (i->j)
Z (Union[float, Callable]) – impedance; a fixed value or function of omega
T (float) – temperature in Kelvin
total (bool) – if False return a time/rate associated with a transition from state i to state j. if True return a time/rate associated with both i to j and j to i transitions
esys (Tuple[ndarray, ndarray]) – evals, evecs tuple
get_rate (bool) – get rate or time
noise_op (ndarray | csc_matrix | Qobj | None)

Returns:

time or rate – decoherence time in units of \(2\pi ({\rm system\,\,units})\), or rate in inverse units.

Return type:

float

t1_effective(noise_channels=None, common_noise_options=None, esys=None, get_rate=False, **kwargs)¶

Calculate the effective \(T_1\) time (or rate).

The effective \(T_1\) is calculated by considering a variety of depolarizing noise channels, according to the formula:

\[\frac{1}{T_{1}^{\rm eff}} = \frac{1}{2} \sum_k \frac{1}{T_{1}^{k}}\]

where \(k\) runs over the channels that can contribute to the effective noise. By default all the depolarizing noise channels given by the method effective_noise_channels are included. Users can also provide specific noise channels, with selected options, to be included in the effective \(T_1\) calculation. For example, assuming qubit is a qubit object, can can execute:

tune_tmon.t1_effective(noise_channels=['t1_charge_impedance',
                        't1_flux_bias_line'],
                        common_noise_options=dict(T=0.050))

Parameters:

noise_channels (Union[str, List[str], List[Tuple[str, Dict]]]) – channels to be plotted, if None then noise channels given by supported_noise_channels are used
common_noise_options (Dict) – common options used when calculating coherence times
esys (Tuple[ndarray, ndarray]) – spectral data used during noise calculations
get_rate (bool) – get rate or time

Return type:

float

Returns:

decoherence time in units of \(2\pi ({\rm system\,\,units})\), or rate: in inverse units.

t1_flux_bias_line(i=1, j=0, M=400, Z=50, T=0.015, total=True, esys=None, get_rate=False, noise_op_method=None)¶

Noise due to a bias flux line.

References: Koch et al (2007), Groszkowski et al (2018)

Parameters:

i (int >=0) – state index that along with j defines a transition (i->j)
j (int >=0) – state index that along with i defines a transition (i->j)
M (float) – Inductance in units of Phi_0 / Ampere
Z (Union[complex, float, Callable]) – A complex impedance; a fixed value or function of omega
T (float) – temperature in Kelvin
total (bool) – if False return a time/rate associated with a transition from state i to state j. if True return a time/rate associated with both i to j and j to i transitions
esys (Tuple[ndarray, ndarray]) – evals, evecs tuple
get_rate (bool) – get rate or time
noise_op_method (Callable | None)

Returns:

time or rate – decoherence time in units of \(2\pi ({\rm system\,\,units})\), or rate in inverse units.

Return type:

float

t1_inductive(i=1, j=0, Q_ind=None, T=0.015, total=True, esys=None, get_rate=False)¶

\(T_1\) due to inductive dissipation in superinductors.

References: nguyen et al (2019), Smith et al (2020)

Parameters:

i (int >=0) – state index that along with j defines a transition (i->j)
j (int >=0) – state index that along with i defines a transition (i->j)
Q_ind (Union[float, Callable]) – inductive quality factor; a fixed value or function of omega
T (float) – temperature in Kelvin
total (bool) – if False return a time/rate associated with a transition from state i to state j. if True return a time/rate associated with both i to j and j to i transitions
esys (Tuple[ndarray, ndarray]) – evals, evecs tuple
get_rate (bool) – get rate or time

Returns:

decoherence time in units of \(2\pi ({\rm system\,\,units})\), or rate in inverse units.

Return type:

time or rate

t1_purcell(i=1, j=0, Q_cap=None, T=0.015, total=True, esys=None, get_rate=False)¶

\(T_1\) due to dielectric dissipation in the shunt capacitor.

References: Nguyen et al (2019), Smith et al (2020)

Parameters:

i (int >=0) – state index that along with j defines a transition (i->j)
j (int >=0) – state index that along with i defines a transition (i->j)
Q_cap (Union[float, Callable]) – capacitive quality factor; a fixed value or function of omega
T (float) – temperature in Kelvin
total (bool) – if False return a time/rate associated with a transition from state i to state j. if True return a time/rate associated with both i to j and j to i transitions
esys (Tuple[ndarray, ndarray]) – evals, evecs tuple
get_rate (bool) – get rate or time

Returns:

decoherence time in units of \(2\pi ({\rm system\,\,units})\), or rate in inverse units.

Return type:

time or rate

t1_quasiparticle_tunneling(i=1, j=0, Y_qp=None, x_qp=3e-06, T=0.015, Delta=0.00034, total=True, esys=None, get_rate=False, noise_op=None)¶

Noise due to quasiparticle tunneling across a Josephson junction.

References: Smith et al (2020), Catelani et al (2011), Pop et al (2014).

Parameters:

i (int >=0) – state index that along with j defines a transition (i->j)
j (int >=0) – state index that along with i defines a transition (i->j)
Y_qp (Union[float, Callable]) – complex admittance; a fixed value or function of omega
x_qp (float) – quasiparticle density (in units of eV)
T (float) – temperature in Kelvin
Delta (float) – superconducting gap (in units of eV)
total (bool) – if False return a time/rate associated with a transition from state i to state j. if True return a time/rate associated with both i to j and j to i transitions
esys (Tuple[ndarray, ndarray]) – evals, evecs tuple
get_rate (bool) – get rate or time
noise_op (ndarray | csc_matrix | Qobj | None)

Returns:

time or rate – decoherence time in units of \(2\pi ({\rm system\,\,units})\), or rate in inverse units.

Return type:

float

t2_effective(noise_channels=None, common_noise_options=None, esys=None, get_rate=False)¶

Calculate the effective \(T_2\) time (or rate).

The effective \(T_2\) is calculated by considering a variety of pure dephasing and depolarizing noise channels, according to the formula:

\[\frac{1}{T_{2}^{\rm eff}} = \sum_k \frac{1}{T_{\phi}^{k}} + \frac{1}{2} \sum_j \frac{1}{T_{1}^{j}},\]

where \(k\) (\(j\)) run over the relevant pure dephasing ( depolarization) channels that can contribute to the effective noise. By default all the noise channels given by the method effective_noise_channels are included. Users can also provide specific noise channels, with selected options, to be included in the effective \(T_2\) calculation. For example, assuming qubit is a qubit object, can can execute:

qubit.t2_effective(noise_channels=['t1_flux_bias_line', 't1_capacitive',
                                   ('tphi_1_over_f_flux', dict(A_noise=3e-6))],
                   common_noise_options=dict(T=0.050))

Parameters:

noise_channels (None or str or list(str) or list(tuple(str, dict))) – channels to be plotted, if None then noise channels given by supported_noise_channels are used
common_noise_options (dict) – common options used when calculating coherence times
esys (tuple(evals, evecs)) – spectral data used during noise calculations
get_rate (bool) – get rate or time

Returns:

time or rate – decoherence time in units of \(2\pi ({\rm system\,\,units})\), or rate in inverse units.

Return type:

float

total_identity()[source]¶

Returns Identity operator acting on the total Hilbert space.

Return type:: csc_matrix

tphi_1_over_f(A_noise, i, j, noise_op, esys=None, get_rate=False, **kwargs)¶

Calculate the 1/f dephasing time (or rate) due to arbitrary noise source.

We assume that the qubit energies (or the passed in eigenspectrum) has units of frequency (and not angular frequency).

Parameters:

A_noise (float) – noise strength
i (int >=0) – state index that along with j defines a qubit
j (int >=0) – state index that along with i defines a qubit
noise_op (Union[ndarray, csc_matrix]) – noise operator, typically Hamiltonian derivative w.r.t. noisy parameter
esys (Tuple[ndarray, ndarray]) – evals, evecs tuple
get_rate (bool) – get rate or time

Returns:

time or rate – decoherence time in units of \(2\pi ({\rm system\,\,units})\), or rate in inverse units.

Return type:

float

tphi_1_over_f_cc(A_noise=1e-07, i=0, j=1, esys=None, get_rate=False, **kwargs)¶

Calculate the 1/f dephasing time (or rate) due to critical current noise.

Parameters:

A_noise (float) – noise strength
i (int >=0) – state index that along with j defines a qubit
j (int >=0) – state index that along with i defines a qubit
esys (Tuple[ndarray, ndarray]) – evals, evecs tuple
get_rate (bool) – get rate or time

Returns:

time or rate – decoherence time in units of \(2\pi ({\rm system\,\,units})\), or rate in inverse units.

Return type:

float

tphi_1_over_f_flux(A_noise=1e-06, i=0, j=1, esys=None, get_rate=False, **kwargs)¶

Calculate the 1/f dephasing time (or rate) due to flux noise.

Parameters:

A_noise (float) – noise strength
i (int >=0) – state index that along with j defines a qubit
j (int >=0) – state index that along with i defines a qubit
esys (Tuple[ndarray, ndarray]) – evals, evecs tuple
get_rate (bool) – get rate or time

Returns:

time or rate – decoherence time in units of \(2\pi ({\rm system\,\,units})\), or rate in inverse units.

Return type:

float

tphi_1_over_f_ng(A_noise=0.0001, i=0, j=1, esys=None, get_rate=False, **kwargs)¶

Calculate the 1/f dephasing time (or rate) due to charge noise.

Parameters:

A_noise (float) – noise strength
i (int >=0) – state index that along with j defines a qubit
j (int >=0) – state index that along with i defines a qubit
esys (Tuple[ndarray, ndarray]) – evals, evecs tuple
get_rate (bool) – get rate or time

Returns:

time or rate – decoherence time in units of \(2\pi ({\rm system\,\,units})\), or rate in inverse units.

Return type:

float

wavefunction(esys=None, which=0, phi_grid=None, zeta_grid=None, theta_grid=None)[source]¶

Return a 3D wave function in \(\phi, \zeta, \theta\) 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

Return type:

WaveFunctionOnGrid

widget(params=None)¶

Use ipywidgets to modify parameters of class instance

Parameters:: params (Dict[str, Any] | None)

zeta_operator(energy_esys=False)[source]¶

Returns the \(\zeta\) operator in the harmonic oscillator or eigenenergy basis.

Parameters:: energy_esys (Union[bool, Tuple[ndarray, ndarray]]) – If False (default), returns \(\zeta\) operator in the native basis. If True, the energy eigenspectrum is computed, returns \(\zeta\) operator in the energy eigenbasis. If energy_esys = esys, where esys is a tuple containing two ndarrays (eigenvalues and energy eigenvectors), returns \(\zeta\) operator in the energy eigenbasis, and does not have to recalculate eigenspectrum.
Return type:: Union[ndarray, csc_matrix]
Returns:: \(\zeta\) operator in chosen basis. If native basis chosen, operator returned as a csc_matrix. If the eigenenergy basis is chosen, unless energy_esys is specified, \(\zeta\) operator has dimensions of truncated_dim x truncated_dim, and is returned as an ndarray. Otherwise, if eigenenergy basis is chosen, \(\zeta\) operator has dimensions of m x m, for m given eigenvectors, and is returned as an ndarray.

zeta_osc()[source]¶

Returns oscillator strength of \(\zeta\) degree of freedom

Return type:: float

zeta_plasma()[source]¶

Returns plasma oscillation frequency of \(\zeta\) degree of freedom

Return type:: float