quara.data_analysis.data_analysis module

calc_covariance_matrix_of_prob_dist(prob_dist, data_num)

calculates covariance matrix of probability distribution.

Parameters

• prob_dist (np.ndarray) – probability distribution.

• data_num (int) – number of data.

Returns

\(\text{covariance matrix} = \frac{1}{len(x)} (diag(p) - p \cdot p^T)\), where N is data_num and p is prob_dist.

Return type

np.ndarray

calc_covariance_matrix_of_prob_dists(prob_dists, data_num)

calculates covariance matrix of probability distributions(= direct product of each covariance matrix of probability distribution).

Parameters

• prob_dists (List[np.ndarray]) – probability distributions.

• data_num (int) – number of data.

Returns

direct product of each covariance matrix = \(\oplus_j V(p^j)\), where \(V(p)\) is covariance matrix of p.

Return type

np.ndarray

calc_estimate_with_average_comp_time(tester_povms, true_object, num_data, iteration, estimator=<class 'quara.protocol.qtomography.standard.standard_qtomography_estimator.StandardQTomographyEstimator'>, on_para_eq_constraint=True)

Parameters

• tester_povms (List[quara.objects.povm.Povm]) –

• true_object (quara.objects.state.State) –

• num_data (List[int]) –

• iteration (int) –

• on_para_eq_constraint (bool) –

Return type

quara.protocol.qtomography.standard.standard_qtomography_estimator.StandardQTomographyEstimationResult

calc_mse_general_norm(xs, y, norm_function)

calculates mse(mean squared error) of xs and y according to norm_function.

Parameters

• xs (np.ndarray) – sample values.

• y (np.ndarray) – true value.

• norm_function (Callable[[np.ndarray, np.ndarray], np.float64]) – norm function.

Returns

\(\text{mse} = \frac{1}{len(x)} \sum_i \text{norm_function}(x_i, y)^2\)

Return type

np.float64

calc_mse_qoperations(xs, ys, mode='qoperation', with_std=True)

Parameters

• xs (List[quara.objects.qoperation.QOperation]) –

• ys (List[quara.objects.qoperation.QOperation]) –

• mode (str) –

• with_std (bool) –

Return type

numpy.float64

convert_to_series(results, true_object)

Parameters

• results (List[quara.protocol.qtomography.standard.standard_qtomography_estimator.StandardQTomographyEstimationResult]) –

• true_object (quara.objects.qoperation.QOperation) –

extract_empi_dists_sequences(source_empi_dists_sequences)

Return type

List[List[List[numpy.ndarray]]]

extract_empi_dists_sequences_old(results)

Parameters

results (List[quara.protocol.qtomography.estimator.EstimationResult]) –

Return type

List[List[List[numpy.ndarray]]]

make_empi_dists_mse_graph(simulation_result, true_object)

Parameters

• simulation_result (quara.simulation.standard_qtomography_simulation.SimulationResult) –

• true_object (quara.objects.qoperation.QOperation) –

make_mses_graph(num_data, mses, error_bar_values_list=None, title='Mean squared error', additional_title_text='', names=None, yaxis_title_text='Mean squared error of estimates and true')

Parameters

• num_data (List[int]) –

• mses (List[List[float]]) –

• error_bar_values_list (List[List[float]]) –

• title (str) –

• additional_title_text (str) –

• names (Optional[List[str]]) –

• yaxis_title_text (str) –

Return type

List[Figure]

make_mses_graph_analytical(estimation_results_list, true_object, estimator_list, num_data, qtomography_list)

Parameters

• estimation_results_list (List[LinearEstimationResult]) –

• estimator_list (list) –

• num_data (List[int]) –

• qtomography_list (List[StandardQTomography]) –

Return type

Figure

make_mses_graph_estimation_results(estimation_results_list, case_names, true_object, num_data, qtomography_list, title='Mean squared error', additional_title_text='', show_analytical_results=False, estimator_list=None)

Parameters

• estimation_results_list (List[LinearEstimationResult]) –

• case_names (List[str]) –

• num_data (List[int]) –

• qtomography_list (List[StandardQTomography]) –

• title (str) –

• additional_title_text (str) –

• show_analytical_results (bool) –

• estimator_list (list) –

Return type

Figure

make_mses_graphs_estimator(estimation_results_list, simulation_settings, true_object, qtomography_list)

Parameters

• estimation_results_list (List[EstimationResult]) –

• simulation_settings (List[StandardQTomographySimulationSetting]) –

• qtomography_list (List[StandardQTomography]) –

Return type

list

make_mses_graphs_para(estimation_results_list, case_names, true_object, num_data, parameter_list, qtomography_list)

Parameters

• estimation_results_list (List[EstimationResult]) –

• case_names (List[str]) –

• true_object (QOperation) –

• num_data (List[int]) –

• parameter_list (List[bool]) –

• qtomography_list (List[StandardQTomography]) –

Return type

list

show_average_computation_times(num_data, computation_times_sequence, num_of_runs, title=None)

Parameters

• num_data (List[int]) –

• computation_times_sequence (List[float]) –

• title (Optional[str]) –

show_computation_times(num_data, computation_times_sequence, title='Computation times for each estimate', histnorm='count')

Parameters

• num_data (List[int]) –

• computation_times_sequence (List[List[float]]) –

• title (str) –

• histnorm (str) –

show_mse(num_data, mses, title='Mean squared error')

Parameters

• num_data (List[int]) –

• mses (List[float]) –

• title (str) –

show_mses(num_data, mses, title='Mean squared error', names=None)

Parameters

• num_data (List[int]) –

• mses (List[List[float]]) –

• title (str) –

• names (Optional[List[str]]) –