quara.protocol.qtomography.standard.standard_qtomography module

class StandardQTomography(experiment, set_qoperations)[source]

Bases: quara.protocol.qtomography.qtomography.QTomography

initialize standard quantum tomography class.

To inherit from this class, set the following instance variables in the constructor of the subclass.

_coeffs_0th: return value of get_coeffs_0th function.
_coeffs_1st: return value of get_coeffs_1st function.
_map_experiment_to_setqoperations: a map from indices of Experiment to indices of SetQOperations.
if you map the 0th state to the 1st state, set {("state", 0): ("state", 1)}.
_map_setqoperations_to_experiment: a map from indices of SetQOperations to indices of Experiment.

Parameters

experiment (Experiment) – Experiment class used in quantum tomography.
set_qoperations (SetQOperations) – SetQOperations class used in quantum tomography.

calc_covariance_linear_mat_total(qope, data_num_list)[source]

calculates covariance matrix of linear estimate of probability distributions.

Parameters

qope (QOperation) – QOperation to calculate covariance matrix of linear estimate of probability distributions.
data_num_list (List[int]) – list of number of data.

Returns

covariance matrix of linear estimate of probability distributions.

Return type

np.ndarray

calc_covariance_mat_single(qope, schedule_index, data_num)[source]

calculates covariance matrix of single probability distribution.

Parameters

qope (QOperation) – QOperation to calculate covariance matrix of single probability distribution.
schedule_index (int) – schedule index.
data_num (int) – number of data.

Returns

covariance matrix of single probability distribution.

Return type

np.ndarray

calc_covariance_mat_total(qope, data_num_list)[source]

calculates covariance matrix of total probability distributions.

Parameters

qope (QOperation) – QOperation to calculate covariance matrix of total probability distributions.
data_num_list (List[int]) – list of number of data.

Returns

covariance matrix of total probability distributions.

Return type

np.ndarray

calc_cramer_rao_bound(var, N, list_N)[source]

calculates Cramer-Rao bound.

Parameters

var (Union[QOperation, np.ndarray]) – variables to calculate Cramer-Rao bound.
N (int) – representative value of the number of data.
list_N (List[int]) – the number of data for each schedule.

Returns

Cramer-Rao bound.

Return type

np.ndarray

calc_fisher_matrix(j, var)[source]

calculates Fisher matrix of one schedule.

Parameters

j (int) – schedule_index
var (Union[QOperation, np.ndarray]) – variables to calculate Fisher matrix of one schedule.

Returns

Fisher matrix of one schedule.

Return type

np.ndarray

calc_fisher_matrix_total(var, weights)[source]

calculates Fisher matrix of the total schedule.

Parameters

var (Union[QOperation, np.ndarray]) – variables to calculate Fisher matrix of one schedule.
weights (List[float]) – weights to calculate Fisher matrix of one schedule.

Returns

Fisher matrix of the total schedule.

Return type

np.ndarray

calc_matA()[source]

returns the matrix A.

the matrix A is a stack of 1st coefficients.

Returns: the matrix A.
Return type: np.ndarray

calc_mse_empi_dists_analytical(qope, data_num_list)[source]

calculates analytical solution of mean squared error of empirical distributions.

Parameters

qope (QOperation) – QOperation to calculate analytical solution of mean squared error of empirical distributions.
data_num_list (List[int]) – list of number of data.

Returns

analytical solution of mean squared error of empirical distributions.

Return type

np.float64

calc_mse_linear_analytical(qope, data_num_list, mode='qoperation')[source]

calculates mean squared error of linear estimate of probability distributions.

Parameters

qope (QOperation) – QOperation to calculate mean squared error of linear estimate of probability distributions.
data_num_list (List[int]) – list of number of data.
mode (str) –

Returns

mean squared error of linear estimate of probability distributions.

Return type

np.float64

calc_prob_dist(qope, schedule_index)[source]

calculates a probability distribution.

see calc_prob_dist()

Parameters

qope (quara.objects.qoperation.QOperation) –
schedule_index (int) –

Return type

List[float]

calc_prob_dists(qope)[source]

calculates probability distributions.

see calc_prob_dists()

Parameters: qope (quara.objects.qoperation.QOperation) –
Return type: List[List[float]]

calc_vecB()[source]

returns the vector B.

the vector B is a stack of 0th coefficients.

Returns: the vector B.
Return type: np.ndarray

abstract convert_var_to_qoperation(var)[source]

converts variable to QOperation.

this function must be implemented in the subclass.

Parameters: var (np.ndarray) – variables.
Returns: converted QOperation.
Return type: QOperation
Raises: NotImplementedError – this function does not be implemented in the subclass.

abstract generate_empty_estimation_obj_with_setting_info()[source]

generates the empty estimation object with setting information.

Returns: the empty estimation object(QOperation) with setting information.
Return type: QOperation
Raises: NotImplementedError – this function does not be implemented in the subclass.

generate_prob_dists_sequence(true_object)[source]

Parameters: true_object (quara.objects.qoperation.QOperation) –
Return type: List[List[Tuple[int, numpy.ndarray]]]

get_coeffs_0th(schedule_index, x)[source]

returns 0th coefficients specified by schedule index and measurement outcome index

Parameters

schedule_index (int) – schedule index.
x (int) – measurement outcome index.

Returns

0th coefficients.

Return type

np.float64

get_coeffs_0th_vec(schedule_index)[source]

returns 0th coefficient vector specified by schedule index.

Parameters: schedule_index (int) – schedule index.
Returns: 0th coefficients vector
Return type: np.ndarray( , dtype=np.float64)

get_coeffs_1st(schedule_index, x)[source]

returns 1st coefficients specified by schedule index and measurement outcome index

Parameters

schedule_index (int) – schedule index.
x (int) – measurement outcome index.

Returns

1st coefficients.

Return type

np.ndarray

get_coeffs_1st_mat(schedule_index)[source]

returns 1st coefficient matrix specified by schedule index.

Parameters: schedule_index (int) – schedule index.
Returns: 1st coefficient matrix.
Return type: np.ndarray

is_all_same_composite_systems(targets)[source]

check all qoperations have same composite systems.

Parameters: targets (List[QOperation]) – list of qoperations.
Returns: whether all qoperations have same composite systems.
Return type: bool

is_fullrank_matA()[source]

returns whether matrix A is full rank.

Returns: True where matrix A is full rank, False otherwise.
Return type: bool

abstract num_outcomes(schedule_index)[source]

returns the number of outcomes of probability distribution of a schedule index.

Parameters: schedule_index (int) –
Returns: the number of outcomes
Return type: int