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Peer-reviewedCC BY 4.0Quantum

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

  • Rick P. A. Simon1
  • Zheng Shi2
  • Charlie Nation1
  • Andrew Jena2,3
  • Luca Dellantonio1
  1. 1Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, UK
  2. 2Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada
  3. 3Department of Combinatorics & Optimization, University of Waterloo, Waterloo, ON N2L 3G1, Canada
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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.

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Cite

BibTeXRIS
BibTeX
@article{simon2026enhanced,
  title = {{Enhanced measurements on quantum computers via the simultaneous probing of non-commuting Pauli operators}},
  author = {Rick P. A. Simon and Zheng Shi and Charlie Nation and Andrew Jena and Luca Dellantonio},
  journal = {Quantum},
  year = {2026},
  month = oct,
  doi = {10.22331/q-2026-10-07-2229},
  url = {https://quantum-journal.org/papers/q-2026-10-07-2229/},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Enhanced measurements on quantum computers via the simultaneous probing of non-commuting Pauli operators
AU  - Rick P. A. Simon
AU  - Zheng Shi
AU  - Charlie Nation
AU  - Andrew Jena
AU  - Luca Dellantonio
PY  - 2026
DA  - 2026/10/07
JO  - Quantum
DO  - 10.22331/q-2026-10-07-2229
UR  - https://quantum-journal.org/papers/q-2026-10-07-2229/
AB  - 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.
SN  - 2521-327X
ER  -