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Classical optimization of reduced density matrix estimations with classical shadows using N-representability conditions under shot noise considerations

Gian-Luca R. Anselmetti*, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, and Michael Streif

  • *Contact author: gian-luca.anselmetti@boehringer-ingelheim.com
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Phys. Rev. Research 8, 033167 – Published 10 August, 2026

DOI: https://doi.org/10.1103/hwcl-yfy4

Abstract

Classical shadow tomography has become a powerful tool in learning about quantum states prepared on a quantum computer. Recent works have used classical shadows to variationally enforce N-representability conditions on the two-particle reduced density matrix. In this paper, we build upon previous research by choosing an improved estimator within classical shadow tomography and rephrasing the optimization constraints, resulting in an overall enhancement in performance under comparable measurement shot budgets. We further explore the specific regimes where these methods outperform the unbiased estimator of the stand-alone classical shadow protocol and quantify the potential savings in numerical studies.

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Outline

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Phys. Rev. Research 8, 033167– Published 10 August, 2026
  • Received 24 October 2025
  • Accepted 14 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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