expectation_value(counts, diagonal=None, qubits=None, clbits=None, meas_mitigator=None)[source]

Compute the expectation value of a diagonal operator from counts.

This computes the estimator of \(\langle O \rangle = \mbox{Tr}[\rho. O]\), optionally with measurement error mitigation, of a diagonal observable \(O = \sum_{x\in\{0, 1\}^n} O(x)|x\rangle\!\langle x|\).

  • counts – counts object

  • diagonal – Optional, the vector of diagonal values for summing the expectation value. If None the the default value is \([1, -1]^\otimes n\).

  • qubits – Optional, the measured physical qubits the count bitstrings correspond to. If None qubits are assumed to be \([0, ..., n-1]\).

  • clbits – Optional, if not None marginalize counts to the specified bits.

  • meas_mitigator – Optional, a measurement mitigator to apply mitigation.


the expectation value and 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 \(O = \mbox{diag}(Z^{\otimes n}) = [1, -1]^{\otimes n}\) 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).

For calibrating a expval measurement error mitigator for the meas_mitigator kwarg see qiskit.ignis.mitigation.expval_meas_mitigator_circuits() and qiskit.ignis.mitigation.ExpvalMeasMitigatorFitter.