Note

This is the documentation for the current state of the development branch of Qiskit Experiments. The documentation or APIs here can change prior to being released.

BlochTrajectoryAnalysis¶

class BlochTrajectoryAnalysis(name=None)[source]¶

A class to analyze a trajectory of the Bloch vector of a single qubit.

Fit model

This is the curve fitting analysis. The following equation(s) are used to represent curve(s).

The following equations are used to approximate the dynamics of the qubit Bloch vector.

\[\begin{split}\begin{align} F_x(t) &= \frac{1}{\Omega^2} \left( - p_z p_x + p_z p_x \cos(\Omega t') + \Omega p_y \sin(\Omega t') \right) + b \tag{1} \\ F_y(t) &= \frac{1}{\Omega^2} \left( p_z p_y - p_z p_y \cos(\Omega t') - \Omega p_x \sin(\Omega t') \right) + b \tag{2} \\ F_z(t) &= \frac{1}{\Omega^2} \left( p_z^2 + (p_x^2 + p_y^2) \cos(\Omega t') \right) + b \tag{3} \end{align}\end{split}\]

where \(t' = t + t_{\rm offset}\) with \(t\) is pulse duration to scan and \(t_{\rm offset}\) is an extra fit parameter that may represent an edge effect. Note that this analysis assumes a microwave drive with the flat top Gaussian envelope, where the amplitude of edges, namely Hamiltonian coefficients of interest, is time dependent and smaller than the flat top part. The edge effect indicates the total net interaction that might be induced by the comparable square drive pulse of duration \(t_{\rm offset}\), which is usually smaller than the actual edge durations.

\(p_x, p_y, p_z, b\) are fit parameters, and \(\Omega = \sqrt{p_x^2+p_y^2+p_z^2}\). The fit functions \(F_x, F_y, F_z\) approximate the Pauli expectation values \(\langle \sigma_x (t) \rangle, \langle \sigma_y (t) \rangle, \langle \sigma_z (t) \rangle\) of the target qubit, respectively.

In this analysis, the initial guess is generated by the following equations.

\[\begin{split}p_x &= \omega \cos(\theta) \cos(\phi) \\ p_y &= \omega \cos(\theta) \sin(\phi) \\ p_z &= \omega \sin(\theta)\end{split}\]

where \(\omega\) is the mean oscillation frequency of eigenvalues, \(\theta = \cos^{-1}\sqrt{\frac{\max F_z - \min F_z}{2}}\) and \(\phi \in [-\pi, \pi]\).

Fit parameters

The following fit parameters are estimated during the analysis.

Descriptions

\(t_{\rm off}\): Offset to the pulse duration. For example, if pulse envelope is a flat-topped Gaussian, two Gaussian edges may become an offset duration.
\(p_x\): Fit parameter of oscillations of the X observable.
\(p_y\): Fit parameter of oscillations of the Y observable.
\(p_z\): Fit parameter of oscillations of the Z observable.
\(b\): Vertical offset of oscillations. This may indicate the state preparation and measurement error.

Initial Guess

\(t_{\rm off}\): Computed as \(N \sqrt{2 \pi} \sigma\) where the \(N\) is number of pulses and \(\sigma\) is Gaussian sigma of rising and falling edges. Note that this implicitly assumes the GaussianSquare pulse envelope.
\(p_x\): See fit model section.
\(p_y\): See fit model section.
\(p_z\): See fit model section.
\(b\): 0

Boundaries

\(t_{\rm off}\): [0, None]
\(p_x\): None
\(p_y\): None
\(p_z\): None
\(b\): None

Analysis options

These are the keyword arguments of the run() method.

Options

Defined in the class BaseCurveAnalysis:
- plotter (BasePlotter)
  
  Default value: Instance of CurvePlotter
  
  A curve plotter instance to visualize the analysis result.
- plot_raw_data (bool)
  
  Default value: False
  
  Set True to draw processed data points, dataset without formatting, on canvas. This is False by default.
- plot_residuals (bool)
  
  Default value: False
  
  Set True to draw the residuals data for the fitting model. This is False by default.
- return_fit_parameters (bool)
  
  Default value: True
  
  (Deprecated) Set True to return all fit model parameters with details of the fit outcome. Default to False.
- data_processor (Callable)
  
  Default value: Instance of DataProcessor
  
  A callback function to format experiment data. This can be a DataProcessor instance that defines the self.__call__ method.
- normalization (bool)
  
  Default value: False
  
  Set True to normalize y values within range [-1, 1]. Default to False.
- average_method (Literal[“sample”, “iwv”, “shots_weighted”])
  
  Default value: "shots_weighted"
  
  Method to average the y values when the same x values appear multiple times. One of “sample”, “iwv” (i.e. inverse weighted variance), “shots_weighted”. See mean_xy_data() for details. Default to “shots_weighted”.
- p0 (Dict[str, float])
  
  Default value: {}
  
  Initial guesses for the fit parameters. The dictionary is keyed on the fit parameter names.
- bounds (Dict[str, Tuple[float, float]])
  
  Default value: {}
  
  Boundary of fit parameters. The dictionary is keyed on the fit parameter names and values are the tuples of (min, max) of each parameter.
- fit_method (str)
  
  Default value: "least_squares"
  
  Fit method that LMFIT minimizer uses. Default to least_squares method which implements the Trust Region Reflective algorithm to solve the minimization problem. See LMFIT documentation for available options.
- lmfit_options (Dict[str, Any])
  
  Default value: {}
  
  Options that are passed to the LMFIT minimizer. Acceptable options depend on fit_method.
- x_key (str)
  
  Default value: "xval"
  
  Circuit metadata key representing a scanned value.
- fit_category (str)
  
  Default value: "formatted"
  
  Name of dataset in the scatter table to fit.
- result_parameters (List[Union[str, ParameterRepr])
  
  Default value: []
  
  Parameters reported in the database as a dedicated entry. This is a list of parameter representation which is either string or ParameterRepr object. If you provide more information other than name, you can specify [ParameterRepr("alpha", "α", "a.u.")] for example. The parameter name should be defined in the series definition. Representation should be printable in standard output, i.e. no latex syntax.
- extra (Dict[str, Any])
  
  Default value: {}
  
  A dictionary that is appended to all database entries as extra information.
- fixed_parameters (Dict[str, Any])
  
  Default value: {}
  
  Fitting model parameters that are fixed during the curve fitting. This should be provided with default value keyed on one of the parameter names in the series definition.
- filter_data (Dict[str, Any])
  
  Default value: {}
  
  Dictionary of experiment data metadata to filter. Experiment outcomes with metadata that matches with this dictionary are used in the analysis. If not specified, all experiment data are input to the curve fitter. By default, no filtering condition is set.
- data_subfit_map (Dict[str, Dict[str, Any]])
  
  Default value: {"x": ("x", {"meas_basis": ("meas_basis", "x")}), "y": ("y", {"meas_basis": ("meas_basis", "y")}), "z": ("z", {"meas_basis": ("meas_basis", "z")})}
  
  The mapping of experiment result data to sub-fit models. This dictionary is keyed on the LMFIT model name, and the value is a sorting key-value pair that filters the experiment results, and the filtering is done based on the circuit metadata.
Defined in the class BaseAnalysis:
- figure_names (str or List[str])
  
  Default value: None
  
  Identifier of figures that appear in the experiment data to sort figures by name.