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Measuring quantum observables by grouping terms that can be rotated to sumsof only products of Pauli $\hat z$ operators (Ising form) is proven to beefficient in near term quantum computing algorithms. This approach requiresextra unitary transformations to rotate the state of interest so that themeasurement of a fragment's Ising form would be equivalent to measurement ofthe fragment for the unrotated state. These extra rotations allow one toperform a fewer number of measurements by grouping more terms into themeasurable fragments with a lower overall estimator variance. However, previousestimations of the number of measurements did not take into account non-unitfidelity of quantum gates implementing the additional transformations. Througha circuit fidelity reduction, additional transformations introduce extrauncertainty and increase the needed number of measurements. Here we consider asimple model for errors introduced by additional gates needed in schemesinvolving grouping of commuting Pauli products. For a set of molecularelectronic Hamiltonians, we confirm that the numbers of measurements in schemesusing non-local qubit rotations are still lower than those in their local qubitrotation counterparts, even after accounting for uncertainties introduced byadditional gates.

Fidelity overhead for non-local measurements in variational quantum algorithms