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class qiskit.result.CorrelatedReadoutMitigator(assignment_matrix, qubits=None)

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N-qubit readout error mitigator.

Mitigates expectation_value() and quasi_probabilities(). The mitigation_matrix should be calibrated using qiskit experiments. This mitigation method should be used in case the readout errors of the qubits are assumed to be correlated. The mitigation_matrix of N qubits is of size $2^N x 2^N$ so the mitigation complexity is $O(4^N)$.

Parameters

• assignment_matrix (ndarray) – readout error assignment matrix.
• qubits (Iterable[int] | None) – Optional, the measured physical qubits for mitigation.

Raises

QiskitError – matrix size does not agree with number of qubits

## Attributes

### qubits

The device qubits for this mitigator

Return settings.

## Methods

### assignment_matrix

assignment_matrix(qubits=None)

Return the readout assignment matrix for specified qubits.

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

Parameters

qubits (List[int] | None) – Optional, qubits being measured.

Returns

the assignment matrix A.

Return type

np.ndarray

### expectation_value

expectation_value(data, diagonal=None, qubits=None, clbits=None, shots=None)

Compute the mitigated expectation value of a diagonal observable.

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

Parameters

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

Returns

the expectation value and an upper bound of the standard deviation.

Return type

(float, float)

The diagonal observable $O$ is input using the diagonal kwarg as a list or Numpy array $[O(0), ..., O(2^n -1)]$. If no diagonal is specified the diagonal of the Pauli operator :mathO = 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

mitigation_matrix(qubits=None)

Return the readout mitigation matrix for the specified qubits.

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

Parameters

qubits (List[int] | None) – Optional, qubits being measured.

Returns

the measurement error mitigation matrix $A^{-1}$.

Return type

np.ndarray

### quasi_probabilities

quasi_probabilities(data, qubits=None, clbits=None, shots=None)

Compute mitigated quasi probabilities value.

Parameters

• data (Counts) – counts object
• qubits (List[int] | None) – qubits the count bitstrings correspond to.
• clbits (List[int] | None) – Optional, marginalize counts to just these bits.
• shots (int | None) – Optional, the total number of shots, if None shots will be calculated as the sum of all counts.

Returns

A dictionary containing pairs of [output, mean] where “output”

is the key in the dictionaries, which is the length-N bitstring of a measured standard basis state, and “mean” is the mean of non-zero quasi-probability estimates.

Return type

QuasiDistribution

### stddev_upper_bound

stddev_upper_bound(shots)

Return an upper bound on standard deviation of expval estimator.

Parameters

shots (int) – Number of shots used for expectation value measurement.

Returns

the standard deviation upper bound.

Return type

float