Learning Quantum Processes with Quantum Statistical Queries

Chirag Wadhwa; Mina Doosti

doi:10.22331/q-2025-05-12-1739

Learning Quantum Processes with Quantum Statistical Queries

Chirag Wadhwa and Mina Doosti

School of Informatics, University of Edinburgh, Edinburgh, United Kingdom

Published:	2025-05-12, volume 9, page 1739
Editor:	Tom Gur
Eprint:	arXiv:2310.02075v4
Doi:	https://doi.org/10.22331/q-2025-05-12-1739
Citation:	Quantum 9, 1739 (2025).

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Abstract

In this work, we initiate the study of learning quantum processes from quantum statistical queries. We focus on two fundamental learning tasks in this new access model: shadow tomography of quantum processes and process tomography with respect to diamond distance. For the former, we present an efficient average-case algorithm along with a nearly matching lower bound with respect to the number of observables to be predicted. For the latter, we present average-case query complexity lower bounds for learning classes of unitaries. We obtain an exponential lower bound for learning unitary 2-designs and a doubly exponential lower bound for Haar-random unitaries. Finally, we demonstrate the practical relevance of our access model by applying our learning algorithm to attack an authentication protocol using Classical-Readout Quantum Physically Unclonable Functions, partially addressing an important open question in quantum hardware security.

Presentation “Learning Quantum Processes with Quantum Statistical Queries – Mina Doosti“

► BibTeX data

@article{Wadhwa2025learningquantum,
  doi = {10.22331/q-2025-05-12-1739},
  url = {https://doi.org/10.22331/q-2025-05-12-1739},
  title = {Learning {Q}uantum {P}rocesses with {Q}uantum {S}tatistical {Q}ueries},
  author = {Wadhwa, Chirag and Doosti, Mina},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1739},
  month = may,
  year = {2025}
}

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Cited by

[1] Chirag Wadhwa, Laura Lewis, Elham Kashefi, and Mina Doosti, "Agnostic Process Tomography", PRX Quantum 6 4, 040371 (2025).

[2] Alexander Nietner, Marios Ioannou, Ryan Sweke, Richard Kueng, Jens Eisert, Marcel Hinsche, and Jonas Haferkamp, "On the average-case complexity of learning output distributions of quantum circuits", Quantum 9, 1883 (2025).

[3] Armando Angrisani, "Learning unitaries with quantum statistical queries", Quantum 9, 1817 (2025).

[4] Martín Larocca, Supanut Thanasilp, Samson Wang, Kunal Sharma, Jacob Biamonte, Patrick J. Coles, Lukasz Cincio, Jarrod R. McClean, Zoë Holmes, and M. Cerezo, "Barren plateaus in variational quantum computing", Nature Reviews Physics 7 4, 174 (2025).

[5] Asad Raza, Matthias C. Caro, Jens Eisert, and Sumeet Khatri, "Online learning of quantum processes", arXiv:2406.04250, (2024).

[6] Alexander Nietner, "Unifying (Quantum) Statistical and Parametrized (Quantum) Algorithms", arXiv:2310.17716, (2023).

[7] Oxana Shaya, Zoë Holmes, Christoph Hirche, and Armando Angrisani, "On the complexity of quantum states and circuits from the orthogonal and symplectic groups", Journal of Physics A Mathematical General 59 20, 205302 (2026).

[8] Kabgyun Jeong, "Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator", arXiv:2606.29487, (2026).

[9] Chirag Wadhwa and Mina Doosti, "Noise-tolerant learnability of shallow quantum circuits from statistics and the cost of quantum pseudorandomness", arXiv:2405.12085, (2024).

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