Process Tomography

class lightworks.tomography.LIProcessTomography(n_qubits: int, base_circuit: PhotonicCircuit)

Bases: _ProcessTomography

Runs quantum process tomography using the linear inversion estimation method.

Parameters:

  • n_qubits (int) – The number of qubits that will be used as part of the tomography.

  • base_circuit (PhotonicCircuit) – An initial circuit which realises the required operation and can be modified for performing tomography. It is required that the number of circuit input modes equals 2 * the number of qubits.

property base_circuit: PhotonicCircuit

The base circuit which the tomography experiment will be performed on.

property choi: ndarray[tuple[int, ...], dtype[complex128]]

Returns the calculate choi matrix for a circuit.

fidelity(choi_exp: ndarray[tuple[int, ...], dtype[complex128]]) → float

Calculates fidelity of the calculated choi matrix compared to the expected one.

get_expected_density_matrices(target_process: ndarray[tuple[int, ...], dtype[complex128]]) → dict[str, ndarray[tuple[int, ...], dtype[complex128]]]

Calculates the expected output density matrices for each input when a target process is applied.

Parameters:

target_process (np.ndarray) – The unitary matrix corresponding to the target process. The dimension of this should be 2^n_qubits.

Returns:

The calculated density matrices for each input.

Return type:

dict

get_experiments() → ProcessTomographyList

Generates all required tomography experiments for performing a process tomography algorithm.

property n_qubits: int

The number of qubits within the system.

process(data: list[dict[State, int]] | dict[tuple[str, str], dict[State, int]]) → ndarray[tuple[int, ...], dtype[complex128]]

Performs process tomography with the configured elements and calculates the choi matrix using linear inversion.

Parameters:

data (list | dict) – The collected measurement data. If a list then this should match the order the experiments were provided, and if a dictionary, then each key should be tuple of the input and measurement basis.

Returns:

The calculated choi matrix for the process.

Return type:

np.ndarray

process_density_matrices(data: list[dict[State, int]] | dict[tuple[str, str], dict[State, int]]) → dict[str, ndarray[tuple[int, ...], dtype[complex128]]]

Calculate and returns the density matrix of the state created for each input to the system.

Parameters:

data (list | dict) – The collected measurement data. If a list then this should match the order the experiments were provided, and if a dictionary, then each key should be tuple of the input and measurement basis.

Returns:

A dictionary of the calculated density matrix for each input

to the system.

Return type:

dict

process_state_fidelities(data: list[dict[State, int]] | dict[tuple[str, str], dict[State, int]], target_process: ndarray[tuple[int, ...], dtype[complex128]]) → dict[str, float]

Calculates the density matrix of the state created for each input to the system and finds the fidelity relative to the expected matrix.

Parameters:

  • data (list | dict) – The collected measurement data. If a list then this should match the order the experiments were provided, and if a dictionary, then each key should be tuple of the input and measurement basis.

  • target_process (np.ndarray) – The unitary matrix corresponding to the target process. The dimension of this should be 2^n_qubits.

Returns:

The calculated fidelity.

Return type:

float

class lightworks.tomography.MLEProcessTomography(n_qubits: int, base_circuit: PhotonicCircuit)

Bases: _ProcessTomography

Runs quantum process tomography using the maximum likelihood estimation method.

Parameters:

  • n_qubits (int) – The number of qubits that will be used as part of the tomography.

  • base_circuit (PhotonicCircuit) – An initial circuit which realises the required operation and can be modified for performing tomography. It is required that the number of circuit input modes equals 2 * the number of qubits.

property base_circuit: PhotonicCircuit

The base circuit which the tomography experiment will be performed on.

property choi: ndarray[tuple[int, ...], dtype[complex128]]

Returns the calculate choi matrix for a circuit.

fidelity(choi_exp: ndarray[tuple[int, ...], dtype[complex128]]) → float

Calculates fidelity of the calculated choi matrix compared to the expected one.

get_expected_density_matrices(target_process: ndarray[tuple[int, ...], dtype[complex128]]) → dict[str, ndarray[tuple[int, ...], dtype[complex128]]]

Calculates the expected output density matrices for each input when a target process is applied.

Parameters:

target_process (np.ndarray) – The unitary matrix corresponding to the target process. The dimension of this should be 2^n_qubits.

Returns:

The calculated density matrices for each input.

Return type:

dict

get_experiments() → ProcessTomographyList

Generates all required tomography experiments for performing a process tomography algorithm.

property n_qubits: int

The number of qubits within the system.

process(data: list[dict[State, int]] | dict[tuple[str, str], dict[State, int]]) → ndarray[tuple[int, ...], dtype[complex128]]

Performs process tomography with the configured elements and calculates the choi matrix using maximum likelihood estimation.

Parameters:

data (list | dict) – The collected measurement data. If a list then this should match the order the experiments were provided, and if a dictionary, then each key should be tuple of the input and measurement basis.

Returns:

The calculated choi matrix for the process.

Return type:

np.ndarray

process_density_matrices(data: list[dict[State, int]] | dict[tuple[str, str], dict[State, int]]) → dict[str, ndarray[tuple[int, ...], dtype[complex128]]]

Calculate and returns the density matrix of the state created for each input to the system.

Parameters:

data (list | dict) – The collected measurement data. If a list then this should match the order the experiments were provided, and if a dictionary, then each key should be tuple of the input and measurement basis.

Returns:

A dictionary of the calculated density matrix for each input

to the system.

Return type:

dict

process_state_fidelities(data: list[dict[State, int]] | dict[tuple[str, str], dict[State, int]], target_process: ndarray[tuple[int, ...], dtype[complex128]]) → dict[str, float]

Calculates the density matrix of the state created for each input to the system and finds the fidelity relative to the expected matrix.

Parameters:

  • data (list | dict) – The collected measurement data. If a list then this should match the order the experiments were provided, and if a dictionary, then each key should be tuple of the input and measurement basis.

  • target_process (np.ndarray) – The unitary matrix corresponding to the target process. The dimension of this should be 2^n_qubits.

Returns:

The calculated fidelity.

Return type:

float

class lightworks.tomography.process_tomography_mle.MLETomographyAlgorithm(n_qubits: int, input_basis: list[str])

Bases: object

Implements the pgdB algorithm for maximum likelihood estimation from https://arxiv.org/abs/1803.10062 for calculation of a physical choi matrix from the tomography measurement data.

Parameters:

n_qubits (int) – The number of qubits used within the tomography.

pgdb(data: dict[tuple[str, str], float], max_iter: int = 1000, stop_threshold: float = 1e-10) → ndarray[tuple[int, ...], dtype[complex128]]

Runs the pgdB algorithm on the provided data set.

Parameters:

  • data (dict) – The measured tomography experiment data. The keys of this dictionary should be the input/measurement basis and the values should be the calculated expectation values.

  • max_iter (int, optional) – Sets the maximum number of iterations that the algorithm can do, defaults to 1000.

  • stop_threshold (float, optional) – Sets the stopping threshold for the gradient descent algorithm. Defaults to 1e-10.

Returns:

The calculated choi matrix

Return type:

np.ndarray