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Noise-induced barren plateaus in variational quantum algorithms

Author

Listed:
  • Samson Wang

    (Los Alamos National Laboratory
    Imperial College London)

  • Enrico Fontana

    (Los Alamos National Laboratory
    University of Strathclyde
    National Physical Laboratory)

  • M. Cerezo

    (Los Alamos National Laboratory
    Los Alamos National Laboratory)

  • Kunal Sharma

    (Los Alamos National Laboratory
    Louisiana State University
    University of Maryland)

  • Akira Sone

    (Los Alamos National Laboratory
    Los Alamos National Laboratory
    Aliro Technologies, Inc)

  • Lukasz Cincio

    (Los Alamos National Laboratory)

  • Patrick J. Coles

    (Los Alamos National Laboratory)

Abstract

Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.

Suggested Citation

  • Samson Wang & Enrico Fontana & M. Cerezo & Kunal Sharma & Akira Sone & Lukasz Cincio & Patrick J. Coles, 2021. "Noise-induced barren plateaus in variational quantum algorithms," Nature Communications, Nature, vol. 12(1), pages 1-11, December.
    • Handle: RePEc:nat:natcom:v:12:y:2021:i:1:d:10.1038_s41467-021-27045-6
    DOI: 10.1038/s41467-021-27045-6
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    3. Eric R. Anschuetz & Bobak T. Kiani, 2022. "Quantum variational algorithms are swamped with traps," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    4. Junyu Liu & Minzhao Liu & Jin-Peng Liu & Ziyu Ye & Yunfei Wang & Yuri Alexeev & Jens Eisert & Liang Jiang, 2024. "Towards provably efficient quantum algorithms for large-scale machine-learning models," Nature Communications, Nature, vol. 15(1), pages 1-6, December.
    5. Bingzhi Zhang & Junyu Liu & Xiao-Chuan Wu & Liang Jiang & Quntao Zhuang, 2024. "Dynamical transition in controllable quantum neural networks with large depth," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
    6. Alen Senanian & Sridhar Prabhu & Vladimir Kremenetski & Saswata Roy & Yingkang Cao & Jeremy Kline & Tatsuhiro Onodera & Logan G. Wright & Xiaodi Wu & Valla Fatemi & Peter L. McMahon, 2024. "Microwave signal processing using an analog quantum reservoir computer," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    7. Enrico Fontana & Dylan Herman & Shouvanik Chakrabarti & Niraj Kumar & Romina Yalovetzky & Jamie Heredge & Shree Hari Sureshbabu & Marco Pistoia, 2024. "Characterizing barren plateaus in quantum ansätze with the adjoint representation," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
    8. Dylan Harley & Ishaun Datta & Frederik Ravn Klausen & Andreas Bluhm & Daniel Stilck França & Albert H. Werner & Matthias Christandl, 2024. "Going beyond gadgets: the importance of scalability for analogue quantum simulators," Nature Communications, Nature, vol. 15(1), pages 1-16, December.
    9. Matthias C. Caro & Hsin-Yuan Huang & M. Cerezo & Kunal Sharma & Andrew Sornborger & Lukasz Cincio & Patrick J. Coles, 2022. "Generalization in quantum machine learning from few training data," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
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    11. Kurowski, Krzysztof & Pecyna, Tomasz & Slysz, Mateusz & Różycki, Rafał & Waligóra, Grzegorz & Wȩglarz, Jan, 2023. "Application of quantum approximate optimization algorithm to job shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 310(2), pages 518-528.
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    15. He, Zhimin & Deng, Maijie & Zheng, Shenggen & Li, Lvzhou & Situ, Haozhen, 2023. "GSQAS: Graph Self-supervised Quantum Architecture Search," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    16. Huang, Chenyi & Zhang, Shibin & Chang, Yan & Yan, Lily, 2024. "Quantum metric learning with fuzzy-informed learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 643(C).
    17. Wang, Shaoxuan & Shen, Yingtong & Liu, Xinjian & Zhang, Haoying & Wang, Yukun, 2024. "Variational quantum entanglement classification discrimination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    18. Michael Ragone & Bojko N. Bakalov & Frédéric Sauvage & Alexander F. Kemper & Carlos Ortiz Marrero & Martín Larocca & M. Cerezo, 2024. "A Lie algebraic theory of barren plateaus for deep parameterized quantum circuits," Nature Communications, Nature, vol. 15(1), pages 1-10, December.
    19. Antoine Jacquier & Oleksiy Kondratyev & Gordon Lee & Mugad Oumgari, 2023. "Quantum Computing for Financial Mathematics," Papers 2311.06621, arXiv.org.
    20. Elies Gil-Fuster & Jens Eisert & Carlos Bravo-Prieto, 2024. "Understanding quantum machine learning also requires rethinking generalization," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
    21. Zhao, Xiumei & Li, Yongmei & Li, Jing & Wang, Shasha & Wang, Song & Qin, Sujuan & Gao, Fei, 2024. "Near-term quantum algorithm for solving the MaxCut problem with fewer quantum resources," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 648(C).
    22. Skavysh, Vladimir & Priazhkina, Sofia & Guala, Diego & Bromley, Thomas R., 2023. "Quantum monte carlo for economics: Stress testing and macroeconomic deep learning," Journal of Economic Dynamics and Control, Elsevier, vol. 153(C).
    23. Fangjun Hu & Saeed A. Khan & Nicholas T. Bronn & Gerasimos Angelatos & Graham E. Rowlands & Guilhem J. Ribeill & Hakan E. Türeci, 2024. "Overcoming the coherence time barrier in quantum machine learning on temporal data," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
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    25. El Amine Cherrat & Snehal Raj & Iordanis Kerenidis & Abhishek Shekhar & Ben Wood & Jon Dee & Shouvanik Chakrabarti & Richard Chen & Dylan Herman & Shaohan Hu & Pierre Minssen & Ruslan Shaydulin & Yue , 2023. "Quantum Deep Hedging," Papers 2303.16585, arXiv.org, revised Nov 2023.

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