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CompleteExpvalMeasMitigator

class CompleteExpvalMeasMitigator(amat)

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Bases: qiskit.ignis.mitigation.expval.base_meas_mitigator.BaseExpvalMeasMitigator

N-qubit measurement error mitigator.

This class can be used with the qiskit.ignis.mitigation.expectation_value() function to apply measurement error mitigation of general N-qubit measurement errors when calculating expectation values from counts. Expectation values can also be computed directly using the expectation_value() method.

For measurement mitigation to be applied the mitigator should be calibrated using the qiskit.ignis.mitigation.expval_meas_mitigator_circuits() function and qiskit.ignis.mitigation.ExpvalMeasMitigatorFitter class with the 'complete' mitigation method.

Initialize a TensorMeasurementMitigator

Parameters

amat (np.array) – readout error assignment matrix.


Methods

assignment_fidelity

CompleteExpvalMeasMitigator.assignment_fidelity(qubits=None)

Return the measurement assignment fidelity on the specified qubits.

The assignment fidelity on N-qubits is defined as x{0,1}nP(xx)/2n\sum_{x\in\{0, 1\}^n} P(x|x) / 2^n, where P(xx)=xAxP(x|x) = \rangle x|A|x\langle, and AA is the assignment_matrix().

Parameters

qubits (Optional[List[int]]) – Optional, qubits being measured for operator expval.

Returns

the assignment fidelity.

Return type

float

assignment_matrix

CompleteExpvalMeasMitigator.assignment_matrix(qubits=None)

Return the measurement assignment matrix for specified qubits.

The assignment matrix is the stochastic matrix AA which assigns a noisy measurement probability distribution to an ideal input measurement distribution: P(ij)=iAjP(i|j) = \langle i | A | j \rangle.

Parameters

qubits (Optional[List[int]]) – Optional, qubits being measured for operator expval.

Returns

the assignment matrix A.

Return type

np.ndarray

expectation_value

CompleteExpvalMeasMitigator.expectation_value(counts, diagonal=None, qubits=None, clbits=None)

Compute the mitigated expectation value of a diagonal observable.

This computes the mitigated estimator of O=Tr[ρ.O]\langle O \rangle = \text{Tr}[\rho. O] of a diagonal observable O=x{0,1}nO(x)x ⁣xO = \sum_{x\in\{0, 1\}^n} O(x)|x\rangle\!\langle x|.

Parameters

  • counts (Dict) – counts object
  • diagonal (Optional[ndarray]) – Optional, the vector of diagonal values for summing the expectation value. If None the the default value is [1,1]n[1, -1]^\otimes n.
  • qubits (Optional[List[int]]) – Optional, the measured physical qubits the count bitstrings correspond to. If None qubits are assumed to be [0,...,n1][0, ..., n-1].
  • clbits (Optional[List[int]]) – Optional, if not None marginalize counts to the specified bits.

Returns

the expectation value and standard deviation.

Return type

(float, float)

Raises

QiskitError – if input arguments are invalid.

Additional Information:

The diagonal observable OO is input using the diagonal kwarg as a list or Numpy array [O(0),...,O(2n1)][O(0), ..., O(2^n -1)]. If no diagonal is specified the diagonal of the Pauli operator :math`O = mbox{diag}(Z^{otimes n}) = [1, -1]^{otimes n}` is used.

The clbits kwarg is used to marginalize the input counts dictionary over the specified bit-values, and the qubits kwarg is used to specify which physical qubits these bit-values correspond to as circuit.measure(qubits, clbits).

mitigation_matrix

CompleteExpvalMeasMitigator.mitigation_matrix(qubits=None)

Return the measurement mitigation matrix for the specified qubits.

The mitigation matrix A1A^{-1} is defined as the inverse of the assignment_matrix() AA.

Parameters

qubits (Optional[List[int]]) – Optional, qubits being measured for operator expval.

Returns

the measurement error mitigation matrix A1A^{-1}.

Return type

np.ndarray

mitigation_overhead

CompleteExpvalMeasMitigator.mitigation_overhead(qubits=None)

Return the mitigation overhead for expectation value estimation.

This is the multiplicative factor of extra shots required for estimating a mitigated expectation value with the same accuracy as an unmitigated expectation value.

Parameters

qubits (Optional[List[int]]) – Optional, qubits being measured for operator expval.

Returns

the mitigation overhead factor.

Return type

int

plot_assignment_matrix

CompleteExpvalMeasMitigator.plot_assignment_matrix(qubits=None, ax=None)

Matrix plot of the readout error assignment matrix.

Parameters

  • qubits (list(int)) – Optional, qubits being measured for operator expval.
  • ax (axes) – Optional. Axes object to add plot to.

Returns

the figure axes object.

Return type

plt.axes

Raises

ImportError – if matplotlib is not installed.

plot_mitigation_matrix

CompleteExpvalMeasMitigator.plot_mitigation_matrix(qubits=None, ax=None)

Matrix plot of the readout error mitigation matrix.

Parameters

  • qubits (list(int)) – Optional, qubits being measured for operator expval.
  • ax (plt.axes) – Optional. Axes object to add plot to.

Returns

the figure axes object.

Return type

plt.axes

Raises

ImportError – if matplotlib is not installed.

required_shots

CompleteExpvalMeasMitigator.required_shots(delta, qubits=None)

Return the number of shots required for expectation value estimation.

This is the number of shots required so that OestOtrue<δ|\langle O \rangle_{est} - \langle O \rangle_{true}| < \delta with high probability (at least 2/3) and is given by 4δ2Γ24\delta^2 \Gamma^2 where Γ2\Gamma^2 is the mitigation_overhead().

Parameters

  • delta (float) – Error tolerance for expectation value estimator.
  • qubits (Optional[List[int]]) – Optional, qubits being measured for operator expval.

Returns

the required shots.

Return type

int

stddev_upper_bound

CompleteExpvalMeasMitigator.stddev_upper_bound(shots=1, qubits=None)

Return an upper bound on standard deviation of expval estimator.

Parameters

  • shots (int) – Number of shots used for expectation value measurement.
  • qubits (Optional[List[int]]) – qubits being measured for operator expval.

Returns

the standard deviation upper bound.

Return type

float

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