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arXiv · 2103.07510

Efficient estimation of Pauli observables by derandomization

Hsin-Yuan Huang·Richard Kueng·John Preskill
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Abstract

We consider the problem of jointly estimating expectation values of many Pauli observables, a crucial subroutine in variational quantum algorithms. Starting with randomized measurements, we propose an efficient derandomization procedure that iteratively replaces random single-qubit measurements with fixed Pauli measurements; the resulting deterministic measurement procedure is guaranteed to perform at least as well as the randomized one. In particular, for estimating any $L$ low-weight Pauli observables, a deterministic measurement on only of order $\log(L)$ copies of a quantum state suffices. In some 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 our derandomized protocol over various previous methods for estimating the ground-state energies of small molecules.

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Hsin-Yuan Huang, Richard Kueng, John Preskill. 2021-03-12. Efficient estimation of Pauli observables by derandomization. https://doi.org/10.1103/physrevlett.127.030503

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