CorrelatedReadoutMitigator

class CorrelatedReadoutMitigator(assignment_matrix, qubits=None)

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 $O(4^N)$.

Initialize a CorrelatedReadoutMitigator

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

settings

Return settings.

Methods

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: $P(i|j)=⟨i|A|j⟩$.

Parameters:

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

Returns:

the assignment matrix A.

Return type:

np.ndarray

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 $⟨O⟩=\text{Tr}[\rho .O]$ of a diagonal observable $O=\sum _{x\in \{0,1{\}}^n}O(x)|x⟩⟨x|$.

Parameters:

• data (Counts) – Counts object

• diagonal (Callable | dict | str | ndarray) – Optional, the vector of diagonal values for summing the expectation value. If None the default value is $[1,-1{]}^{\otimes }n$.

• qubits (Iterable[int]) – 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)

Additional Information:

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 :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(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]) – Optional, qubits being measured.

Returns:

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

Return type:

np.ndarray

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(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