Quantum memory assisted observable estimation

Liubov A. Markovich; Attaallah Almasi; Sina Zeytinoğlu; Johannes Borregaard

doi:10.22331/q-2025-03-06-1655

Quantum memory assisted observable estimation

Liubov A. Markovich¹, Attaallah Almasi², Sina Zeytinoğlu^3,4, and Johannes Borregaard⁵

¹Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
²QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
³Physics and Informatics Laboratory, NTT Research, Inc., Sunnyvale, California, 94085, The USA
⁴Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria
⁵Department of Physics, Harvard University, Cambridge, MA 02138, USA

Published:	2025-03-06, volume 9, page 1655
Editor:	Carlo Beenakker
Eprint:	arXiv:2212.07710v4
Doi:	https://doi.org/10.22331/q-2025-03-06-1655
Citation:	Quantum 9, 1655 (2025).

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Updated version: The authors have uploaded version v5 of this work to the arXiv which may contain updates or corrections not contained in the published version v4. The authors left the following comment on the arXiv:

21 pages, 2 figures

Abstract

The estimation of many-qubit observables is an essential task of quantum information processing. The generally applicable approach is to decompose the observables into weighted sums of multi-qubit Pauli strings, i.e., tensor products of single-qubit Pauli matrices, which can readily be measured with low-depth Clifford circuits. The accumulation of shot noise in this approach, however, severely limits the achievable variance for a finite number of measurements. We introduce a novel method, dubbed $\textit{coherent Pauli summation}$ (CPS), that circumvents this limitation by exploiting access to a single-qubit quantum memory in which measurement information can be stored and accumulated. CPS offers a reduction in the required number of measurements for a given variance that scales linearly with the number of Pauli strings in the decomposed observable. Our work demonstrates how a single long-coherence qubit memory can assist the operation of many-qubit quantum devices in a cardinal task.

► BibTeX data

@article{Markovich2025quantummemory,
  doi = {10.22331/q-2025-03-06-1655},
  url = {https://doi.org/10.22331/q-2025-03-06-1655},
  title = {Quantum memory assisted observable estimation},
  author = {Markovich, Liubov A. and Almasi, Attaallah and Zeytino{\u{g}}lu, Sina and Borregaard, Johannes},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1655},
  month = mar,
  year = {2025}
}

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[1] Liubov Markovich, Savvas Malikis, Stefano Polla, and Jordi Tura, "Parameter shift rule with optimal phase selection", Physical Review A 109 6, 062429 (2024).

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