Classical Shadows With Noise

Dax Enshan Koh; Sabee Grewal

doi:10.22331/q-2022-08-16-776

Classical Shadows With Noise

¹Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore
²Zapata Computing, Inc., 100 Federal Street, 20th Floor, Boston, Massachusetts 02110, USA
³Department of Computer Science, The University of Texas at Austin, Austin, TX 78712, USA

Published:	2022-08-16, volume 6, page 776
Eprint:	arXiv:2011.11580v2
Doi:	https://doi.org/10.22331/q-2022-08-16-776
Citation:	Quantum 6, 776 (2022).

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Abstract

The classical shadows protocol, recently introduced by Huang, Kueng, and Preskill [Nat. Phys. 16, 1050 (2020)], is a quantum-classical protocol to estimate properties of an unknown quantum state. Unlike full quantum state tomography, the protocol can be implemented on near-term quantum hardware and requires few quantum measurements to make many predictions with a high success probability.

In this paper, we study the effects of noise on the classical shadows protocol. In particular, we consider the scenario in which the quantum circuits involved in the protocol are subject to various known noise channels and derive an analytical upper bound for the sample complexity in terms of a shadow seminorm for both local and global noise. Additionally, by modifying the classical post-processing step of the noiseless protocol, we define a new estimator that remains unbiased in the presence of noise. As applications, we show that our results can be used to prove rigorous sample complexity upper bounds in the cases of depolarizing noise and amplitude damping.

► BibTeX data

@article{Koh2022classicalshadows,
  doi = {10.22331/q-2022-08-16-776},
  url = {https://doi.org/10.22331/q-2022-08-16-776},
  title = {Classical {S}hadows {W}ith {N}oise},
  author = {Koh, Dax Enshan and Grewal, Sabee},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {776},
  month = aug,
  year = {2022}
}

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