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Barren plateaus in quantum neural network training landscapes

Author

Listed:
  • Jarrod R. McClean

    (Google Inc.)

  • Sergio Boixo

    (Google Inc.)

  • Vadim N. Smelyanskiy

    (Google Inc.)

  • Ryan Babbush

    (Google Inc.)

  • Hartmut Neven

    (Google Inc.)

Abstract

Many experimental proposals for noisy intermediate scale quantum devices involve training a parameterized quantum circuit with a classical optimization loop. Such hybrid quantum-classical algorithms are popular for applications in quantum simulation, optimization, and machine learning. Due to its simplicity and hardware efficiency, random circuits are often proposed as initial guesses for exploring the space of quantum states. We show that the exponential dimension of Hilbert space and the gradient estimation complexity make this choice unsuitable for hybrid quantum-classical algorithms run on more than a few qubits. Specifically, we show that for a wide class of reasonable parameterized quantum circuits, the probability that the gradient along any reasonable direction is non-zero to some fixed precision is exponentially small as a function of the number of qubits. We argue that this is related to the 2-design characteristic of random circuits, and that solutions to this problem must be studied.

Suggested Citation

  • Jarrod R. McClean & Sergio Boixo & Vadim N. Smelyanskiy & Ryan Babbush & Hartmut Neven, 2018. "Barren plateaus in quantum neural network training landscapes," Nature Communications, Nature, vol. 9(1), pages 1-6, December.
    • Handle: RePEc:nat:natcom:v:9:y:2018:i:1:d:10.1038_s41467-018-07090-4
    DOI: 10.1038/s41467-018-07090-4
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    Cited by:

    1. Manuel S. Rudolph & Jacob Miller & Danial Motlagh & Jing Chen & Atithi Acharya & Alejandro Perdomo-Ortiz, 2023. "Synergistic pretraining of parametrized quantum circuits via tensor networks," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    2. 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.
    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. Camille Grange & Michael Poss & Eric Bourreau, 2023. "An introduction to variational quantum algorithms for combinatorial optimization problems," 4OR, Springer, vol. 21(3), pages 363-403, September.
    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. Wei-Ming Li & Shi-Ju Ran, 2022. "Non-Parametric Semi-Supervised Learning in Many-Body Hilbert Space with Rescaled Logarithmic Fidelity," Mathematics, MDPI, vol. 10(6), pages 1-15, March.
    8. 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.
    9. Amine Assouel & Antoine Jacquier & Alexei Kondratyev, 2021. "A Quantum Generative Adversarial Network for distributions," Papers 2110.02742, arXiv.org.
    10. Aritra Sarkar & Zaid Al-Ars & Koen Bertels, 2021. "QuASeR: Quantum Accelerated de novo DNA sequence reconstruction," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-23, April.
    11. 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.
    12. 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).
    13. Pinaki Sen & Amandeep Singh Bhatia & Kamalpreet Singh Bhangu & Ahmed Elbeltagi, 2022. "Variational quantum classifiers through the lens of the Hessian," PLOS ONE, Public Library of Science, vol. 17(1), pages 1-17, January.
    14. Ajagekar, Akshay & You, Fengqi, 2022. "Quantum computing and quantum artificial intelligence for renewable and sustainable energy: A emerging prospect towards climate neutrality," Renewable and Sustainable Energy Reviews, Elsevier, vol. 165(C).
    15. Takayuki Sakuma, 2020. "Application of deep quantum neural networks to finance," Papers 2011.07319, arXiv.org, revised May 2022.
    16. 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.
    17. 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.
    18. 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).
    19. 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.
    20. Sofiene Jerbi & Lukas J. Fiderer & Hendrik Poulsen Nautrup & Jonas M. Kübler & Hans J. Briegel & Vedran Dunjko, 2023. "Quantum machine learning beyond kernel methods," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    21. Liu, Ling & Song, Tingting & Sun, Zhiwei & Lei, Jiancheng, 2022. "Quantum generative adversarial networks based on Rényi divergences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    22. Iris Cong & Nishad Maskara & Minh C. Tran & Hannes Pichler & Giulia Semeghini & Susanne F. Yelin & Soonwon Choi & Mikhail D. Lukin, 2024. "Enhancing detection of topological order by local error correction," Nature Communications, Nature, vol. 15(1), pages 1-14, December.
    23. 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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