qiskit.ignis.verification.StateTomographyFitter¶

class StateTomographyFitter(result, circuits, meas_basis='Pauli')[source]¶

Maximum-Likelihood estimation state tomography fitter.

Initialize state tomography fitter with experimental data.

Parameters

result (Result) – a Qiskit Result object obtained from executing tomography circuits.
circuits (List[QuantumCircuit]) – a list of circuits or circuit names to extract count information from the result object.
meas_basis (Union[TomographyBasis, str]) – (default: ‘Pauli’) A function to return measurement operators corresponding to measurement outcomes. See Additional Information (default: ‘Pauli’)

__init__(result, circuits, meas_basis='Pauli')[source]¶

Initialize state tomography fitter with experimental data.

Parameters

result (Result) – a Qiskit Result object obtained from executing tomography circuits.
circuits (List[QuantumCircuit]) – a list of circuits or circuit names to extract count information from the result object.
meas_basis (Union[TomographyBasis, str]) – (default: ‘Pauli’) A function to return measurement operators corresponding to measurement outcomes. See Additional Information (default: ‘Pauli’)

Methods

`__init__`(result, circuits[, meas_basis])	Initialize state tomography fitter with experimental data.
`add_data`(results, circuits)	Add tomography data from a Qiskit Result object.
`fit`([method, standard_weights, beta])	Reconstruct a quantum state using CVXPY convex optimization.
`set_measure_basis`(basis)	Set the measurement basis
`set_preparation_basis`(basis)	Set the preparation basis function

Attributes

`data`	Return tomography data
`measure_basis`	Return the tomography measurement basis.
`preparation_basis`	Return the tomography preparation basis.

add_data(results, circuits)¶

Add tomography data from a Qiskit Result object.

Parameters

results (List[Result]) – The results obtained from executing tomography circuits.
circuits (List[Union[QuantumCircuit, str]]) – circuits or circuit names to extract count information from the result object.

Raises

QiskitError – In case some of the tomography data is not found in the results

property data¶: Return tomography data

fit(method='auto', standard_weights=True, beta=0.5, **kwargs)[source]¶

Reconstruct a quantum state using CVXPY convex optimization.

Fitter method

The cvx fitter method used CVXPY convex optimization package. The lstsq method uses least-squares fitting (linear inversion). The auto method will use ‘cvx’ if the CVXPY package is found on the system, otherwise it will default to ‘lstsq’.

Objective function

This fitter solves the constrained least-squares minimization: \(minimize: ||a \cdot x - b ||_2\)

subject to:

\(x >> 0\)

\(\text{trace}(x) = 1\)

where:

a is the matrix of measurement operators \(a[i] = \text{vec}(M_i).H\)

b is the vector of expectation value data for each projector \(b[i] \sim \text{Tr}[M_i.H \cdot x] = (a \cdot x)[i]\)

x is the vectorized density matrix to be fitted

PSD constraint

The PSD keyword constrains the fitted matrix to be postive-semidefinite. For the lstsq fitter method the fitted matrix is rescaled using the method proposed in Reference [1]. For the cvx fitter method the convex constraint makes the optimization problem a SDP. If PSD=False the fitted matrix will still be constrained to be Hermitian, but not PSD. In this case the optimization problem becomes a SOCP.

Trace constraint

The trace keyword constrains the trace of the fitted matrix. If trace=None there will be no trace constraint on the fitted matrix. This constraint should not be used for process tomography and the trace preserving constraint should be used instead.

CVXPY Solvers:

Various solvers can be called in CVXPY using the solver keyword argument. See the CVXPY documentation for more information on solvers.

References:

[1] J Smolin, JM Gambetta, G Smith, Phys. Rev. Lett. 108, 070502: (2012). Open access: arXiv:1106.5458 [quant-ph].

Parameters

method (str) – The fitter method ‘auto’, ‘cvx’ or ‘lstsq’.
standard_weights (bool) – (default: True) Apply weights to tomography data based on count probability
beta (float) – (default: 0.5) hedging parameter for converting counts to probabilities
**kwargs – kwargs for fitter method.

Raises

QiskitError – In case the fitting method is unrecognized.

Return type

array

Returns

The fitted matrix rho that minimizes \(||\text{basis_matrix} \cdot \text{vec}(\text{rho}) - \text{data}||_2\).

property measure_basis¶: Return the tomography measurement basis.

property preparation_basis¶: Return the tomography preparation basis.

set_measure_basis(basis)¶

Set the measurement basis

Parameters: basis (Union[TomographyBasis, str]) – measurement basis
Raises: QiskitError – In case of invalid measurement or preparation basis.

set_preparation_basis(basis)¶

Set the preparation basis function

Parameters: basis (Union[TomographyBasis, str]) – preparation basis
Raises: QiskitError – in case the basis has no preperation data