qsttoolkit.tomography Subpackage

This subpackage contains models for performing quantum state tomography. Each model is implemented in its own class, each inheriting basic performance analysis and plotting functions from a parent class qsttoolkit.tomography.QST.

The fundamental aim of QSTToolkit is to provide modular, ‘drag-and-drop’ functions for researching, testing and comparing quantum state tomography methods in different experimental situations. This is enabled by the CustomQuantumStateTomography class, which allows a user to define a single pass of their own custom tomography training loop. Experimentation with combinations of tomography components is encouraged - for example, using a generator model with a different density matrix parametrization and loss function.

Traditional QST

Traditional quantum state tomography is implemented using Maximum Likelihood Estimation (MLE):

• Maximum Likelihood Estimation (MLE) Quantum State Tomography
  • MLEQuantumStateTomography
  • train()
  • train_step()

Deep Learning QST

Four deep learning models are currently implemented using TensorFlow: one for quantum state discrimination and three for quantum state tomography. Each model has a dedicated class:

• Convolutional Neural Network (CNN) Quantum State Discrimination
  • build_classifier()
  • CNNQuantumStateDiscrimination
• Generative Adversarial Network (GAN) Quantum State Tomography
  • CholeskyLowerTriangular
  • DensityMatrix
  • build_discriminator()
  • build_generator()
  • GANQuantumStateTomography
  • train()
• Multitask Regression/Classification Network Quantum State Reconstruction
  • build_classification_tail()
  • build_feature_extractor()
  • build_multitask_reconstructor()
  • build_regression_tail()
  • MultitaskQuantumStateTomography
  • StateReconstructor

Global QST Utility Functions

Functions used in both traditional and deep learning methods for quantum state tomography.

class qsttoolkit.tomography.QST.CustomQuantumStateTomography(model, training_step_fn)

Bases: QuantumStateTomography

A class for designing custom quantum state tomography methods.

model

Model used for the reconstruction.

Type:

tf.keras.Model

training_step_fn

Function that defines the training step for the model. Arguments must include [model, measurement_data, measurement_operators]. Must return the generated density matrix and the loss.

Type:

callable

reconstruct(measurement_data, measurement_operators, epochs, optimizer, verbose_interval: int = None, num_progress_saves: int = None, true_dm: Tensor = None, time_log_interval: int = None, **kwargs)

Reconstructs the density matrix using a custom method.

Parameters:

• initial_dm (np.ndarray) – Initial density matrix.

• measurement_data (np.ndarray) – Frequency of each measurement outcome.

• measurement_operators (np.ndarray) – Projective operators corresponding to the measurement outcomes.

• epochs (int) – Number of training epochs.

• optimizer (tf.keras.optimizers.Optimizer) – Optimizer for the training step.

• verbose_interval (int) – Interval at which to print progress updates. Defaults to None.

• num_progress_saves (int) – Number of intermediate progress saves to make. Defaults to None.

• true_dm (tf.Tensor) – True density matrix used for calculating fidelities. Defaults to None.

• time_log_interval (int) – Interval at which to log the time taken after each epoch. Defaults to None.

class qsttoolkit.tomography.QST.QuantumStateTomography

Bases: object

A parent class for all quantum state tomography methods.

fidelity(true_dm: ndarray) → float

Computes the fidelity between the true and reconstructed density matrices.

Parameters:

true_dm (np.ndarray) – True density matrix.

Returns:

Fidelity between the true and reconstructed density matrices.

Return type:

float

plot_comparison_Hintons(true_dm: ndarray)

Deprecated alias for plot_comparison_hintons. Plots Hinton diagrams of the true and reconstructed density matrices.

plot_comparison_Husimi_Qs(true_dm: ndarray, xgrid: ndarray, pgrid: ndarray)

Deprecated alias for plot_comparison_husimi_Qs. Plots the Husimi Q functions of the true and reconstructed density matrices.

plot_comparison_hintons(true_dm: ndarray)

Plots Hinton diagrams of the true and reconstructed density matrices.

Parameters:

true_dm (np.ndarray) – True density matrix.

plot_comparison_husimi_Qs(true_dm: ndarray, xgrid: ndarray, pgrid: ndarray)

Plots the Husimi Q functions of the true and reconstructed density matrices.

Parameters:

• true_dm (np.ndarray) – True density matrix.

• xgrid (np.ndarray) – Phase space X quadrature grid.

• pgrid (np.ndarray) – Phase space P quadrature grid.

plot_comparison_wigners(true_dm: ndarray, xgrid: ndarray, pgrid: ndarray)

Plots the Wigner functions of the true and reconstructed density matrices.

Parameters:

• true_dm (np.ndarray) – True density matrix.

• xgrid (np.ndarray) – Phase space X quadrature grid.

• pgrid (np.ndarray) – Phase space P quadrature grid.

plot_fidelities(true_dm=None)

Plots the fidelity between the true and reconstructed density matrices over epochs.

plot_intermediate_Hintons()

Deprecated alias for plot_intermediate_hintons. Plots Hinton diagrams of the density matrices in the progress_saves attribute.

plot_intermediate_Husimi_Qs(xgrid: ndarray, pgrid: ndarray)

Deprecated alias for plot_intermediate_husimi_Qs. Plots the Husimi Q functions of the density matrices in the progress_saves attribute.

plot_intermediate_hintons()

Plots Hinton diagrams of the density matrices in the progress_saves attribute.

plot_intermediate_husimi_Qs(xgrid: ndarray, pgrid: ndarray)

Plots the Husimi Q functions of the density matrices in the progress_saves attribute.

Parameters:

• xgrid (np.ndarray) – Phase space X quadrature grid.

• pgrid (np.ndarray) – Phase space P quadrature grid.

plot_intermediate_wigners(xgrid: ndarray, pgrid: ndarray)

Plots the Wigner functions of the density matrices in the progress_saves attribute.

Parameters:

• xgrid (np.ndarray) – Phase space X quadrature grid.

• pgrid (np.ndarray) – Phase space P quadrature grid.

plot_losses()

Plots the losses over epochs.

plot_times()

Plots the cumulative time taken for each epoch.

qsttoolkit.tomography.QST.parameterise_density_matrix(rho: Tensor) → Tensor

Deprecated alias for parametrize_density_matrix.

qsttoolkit.tomography.QST.parametrize_density_matrix(rho: Tensor) → Tensor

parametrizes the density matrix using the Cholesky decomposition.

Parameters:

rho (tf.Tensor) – Density matrix to be parametrized.

Returns:

Cholesky decomposition of the density matrix.

Return type:

tf.Tensor

qsttoolkit.tomography.QST.positivity_constraint(params: ndarray) → float

Constraint to ensure the density matrix is positive semi-definite.

Parameters:

params (np.ndarray) – Flattened vector of real parameters.

Returns:

Smallest eigenvalue of the reconstructed density matrix.

Return type:

float

qsttoolkit.tomography.QST.reconstruct_density_matrix(params: Tensor, reg: float = 1e-10, dim=None) → Tensor

Reconstructs the density matrix from the Cholesky decomposition.

Parameters:

params (tf.Tensor) – Cholesky decomposition of the density matrix.

Returns:

Reconstructed density matrix.

Return type:

tf.Tensor

qsttoolkit.tomography.QST.trace_constraint(params: ndarray) → float

Constraint function to ensure the trace of the density matrix is 1.

Parameters:

params (np.ndarray) – Flattened vector of real parameters.

Returns:

Difference between the trace of the reconstructed density matrix and 1.

Return type:

float

Loss Functions

qsttoolkit.tomography.loss.kl_divergence(rho: Tensor, frequency_data: Tensor, measurement_operators: list, L1_reg: float = 0, thresh_reg: float = 0, thresh_reg_threshold: float = 0.01) → Tensor

Computes the Kullback-Leibler divergence of the data given the density matrix.

Parameters:

• rho (tf.Tensor) – Density matrix.

• frequency_data (tf.Tensor) – Frequency of each measurement outcome.

• measurement_operators (list of Qobj) – Projective measurement operators corresponding to the measurement outcomes.

• L1_reg (float) – L1 regularisation parameter. Defaults to 0.

• thresh_reg (float) – Threshold regularisation parameter. Defaults to 0.

• thresh_reg_threshold (float) – Threshold for the threshold regularisation. Defaults to 0.01.

Returns:

Kullback-Leibler divergence of the data given the density matrix.

Return type:

tf.Tensor

qsttoolkit.tomography.loss.log_likelihood(rho: Tensor, frequency_data: Tensor, measurement_operators: list, L1_reg: float = 0, thresh_reg: float = 0, thresh_reg_threshold: float = 0.01, dim=None) → Tensor

Computes the negative log-likelihood of the data given the density matrix.

Parameters:

• rho (tf.Tensor) – Density matrix.

• frequency_data (tf.Tensor) – Frequency of each measurement outcome.

• measurement_operators (list of Qobj) – Projective measurement operators corresponding to the measurement outcomes.

• L1_reg (float) – L1 regularisation parameter. Defaults to 0.

• thresh_reg (float) – Threshold regularisation parameter. Defaults to 0.

• thresh_reg_threshold (float) – Threshold for the threshold regularisation. Defaults to 0.01.

Returns:

negative log-likelihood of the data given the density matrix.

Return type:

tf.Tensor

qsttoolkit.tomography.loss.mean_absolute_error(rho: Tensor, frequency_data: Tensor, measurement_operators: list, L1_reg: float = 0, thresh_reg: float = 0, thresh_reg_threshold: float = 0.01) → Tensor

Computes the mean absolute error of the data given the density matrix.

Parameters:

• rho (tf.Tensor) – Density matrix.

• frequency_data (tf.Tensor) – Frequency of each measurement outcome.

• measurement_operators (list of Qobj) – Projective measurement operators corresponding to the measurement outcomes.

• L1_reg (float) – L1 regularisation parameter. Defaults to 0.

• thresh_reg (float) – Threshold regularisation parameter. Defaults to 0.

• thresh_reg_threshold (float) – Threshold for the threshold regularisation. Defaults to 0.01.

Returns:

Mean absolute error of the data given the density matrix.

Return type:

tf.Tensor

qsttoolkit.tomography.loss.mean_squared_error(rho: Tensor, frequency_data: Tensor, measurement_operators: list, L1_reg: float = 0, thresh_reg: float = 0, thresh_reg_threshold: float = 0.01) → Tensor

Computes the mean squared error of the data given the density matrix.

Parameters:

• rho (tf.Tensor) – Density matrix.

• frequency_data (tf.Tensor) – Frequency of each measurement outcome.

• measurement_operators (list of Qobj) – Projective measurement operators corresponding to the measurement outcomes.

• L1_reg (float) – L1 regularisation parameter. Defaults to 0.

• thresh_reg (float) – Threshold regularisation parameter. Defaults to 0.

• thresh_reg_threshold (float) – Threshold for the threshold regularisation. Defaults to 0.01.

Returns:

Mean squared error of the data given the density matrix.

Return type:

tf.Tensor

qsttoolkit.tomography.loss.squared_hellinger_distance(rho: Tensor, frequency_data: Tensor, measurement_operators: list, L1_reg: float = 0, thresh_reg: float = 0, thresh_reg_threshold: float = 0.01) → Tensor

Computes the squared Hellinger distance of the data given the density matrix.

Parameters:

• rho (tf.Tensor) – Density matrix.

• frequency_data (tf.Tensor) – Frequency of each measurement outcome.

• measurement_operators (list of Qobj) – Projective measurement operators corresponding to the measurement outcomes.

• L1_reg (float) – L1 regularisation parameter. Defaults to 0.

• thresh_reg (float) – Threshold regularisation parameter. Defaults to 0.

• thresh_reg_threshold (float) – Threshold for the threshold regularisation. Defaults to 0.01.

Returns:

Squared Hellinger distance of the data given the density matrix.

Return type:

tf.Tensor