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We consider the problem of jointly estimating expectation values of manyPauli observables, a crucial subroutine in variational quantum algorithms.Starting with randomized measurements, we propose an efficient derandomizationprocedure that iteratively replaces random single-qubit measurements with fixedPauli measurements; the resulting deterministic measurement procedure isguaranteed to perform at least as well as the randomized one. In particular,for estimating any $L$ low-weight Pauli observables, a deterministicmeasurement on only of order $\log(L)$ copies of a quantum state suffices. Insome cases, for example when some of the Pauli observables have a high weight,the derandomized procedure is substantially better than the randomized one.Specifically, numerical experiments highlight the advantages of ourderandomized protocol over various previous methods for estimating theground-state energies of small molecules.

Efficient estimation of Pauli observables by derandomization