Enhanced measurements on quantum computers via the simultaneous probing of non-commuting Pauli operators

Abstract:Measuring the state of quantum computers is a highly non-trivial task, with implications for virtually all quantum algorithms. A promising avenue is multi-copy schemes, where identical copies of a quantum state are measured jointly so that all Pauli operators within the considered observable can be simultaneously assessed. Here, we present a first implementation of such a two-copy scheme in a measurement protocol. Based on Bayesian statistics, it accurately estimates not only the average of the desired observable but also the error en route. This enables an adaptive shot-allocation algorithm that preferentially samples the most uncertain Pauli terms. In regimes with many non-commuting Pauli operators, this ``double'' scheme can outperform the state-of-the-art measurement protocol in minimizing total shots for a given precision. We also numerically confirm the finding in previous theoretical works that the two-copy scheme incurs an overhead due to the square-root relationship between the variance of measured quantities and the number of measurement shots.

6 pages main text, 2 pages supplemental information, 2 figures. Comments are welcome :)

arXiv:2509.01482 [quant-ph]

(or arXiv:2509.01482v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2509.01482 Focus to learn more arXiv-issued DOI via DataCite

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