qiskit.ignis.verification.StateTomographyFitter¶

class
StateTomographyFitter
(result, circuits, meas_basis='Pauli')[source]¶ MaximumLikelihood 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
Return tomography data
Return the tomography measurement 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. Thelstsq
method uses leastsquares fitting (linear inversion). Theauto
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 leastsquares 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 postivesemidefinite. For the
lstsq
fitter method the fitted matrix is rescaled using the method proposed in Reference [1]. For thecvx
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 [quantph].
 Parameters
method (
str
) – The fitter method ‘auto’, ‘cvx’ or ‘lstsq’.standard_weights (
bool
) – (default: True) Apply weights to tomography data based on count probabilitybeta (
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