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Layerwise learning for quantum neural networks
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Abstract With the increased focus on quantum circuit learning for near-term applications on quantum devices, in conjunction with unique challenges presented by cost function landscapes of parametrized quantum circuits, strategies for effective training are becoming increasingly important. In order to ameliorate some of these challenges, we investigate a layerwise learning strategy for parametrized quantum circuits. The circuit depth is incrementally grown during optimization, and only subsets of parameters are updated in each training step. We show that when considering sampling noise, this strategy can help avoid the problem of barren plateaus of the error surface due to the low depth of circuits, low number of parameters trained in one step, and larger magnitude of gradients compared to training the full circuit. These properties make our algorithm preferable for execution on noisy intermediate-scale quantum devices. We demonstrate our approach on an image-classification task on handwritten digits, and show that layerwise learning attains an 8% lower generalization error on average in comparison to standard learning schemes for training quantum circuits of the same size. Additionally, the percentage of runs that reach lower test errors is up to 40% larger compared to training the full circuit, which is susceptible to creeping onto a plateau during training.
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“Additionally, in Refs. [29, 205] an initialization strategy was developed specifically to address BPs in deep circuits. Here, one selects at random a subset of parameters in θ , and chooses the value of the remaining ones so that the circuit is a sequence of shallow unitaries that evaluates to the identity.”
From Variational quantum algorithms (2021) · cites this paper as [205]
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“Regardless of the conditions of their advantages, these approaches need careful consideration of subtle issues (see, e.g., Refs.[112-115]) that do not appear in classical algorithms and are, in particular, strongly intertwined with the underlying hardware.”
From Neutral atom quantum computing hardware: performance and end-user perspective (2023) · cites this paper as [113]
In the citing paper
“It was found that the entries of the Hessian vanish exponentially with the size of the system in models that are in a barren plateau.”
From The power of quantum neural networks (2021) · cites this paper as [32]
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“In the quantum realm, the negative effect of barren plateaus on training quantum neural networks has been linked to the Hessian matrix [32].”
From The power of quantum neural networks (2021) · cites this paper as [32]
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Gibbs, J., Gili, K., Holmes, Z., Commeau, B., Arrasmith, A., Cincio, L., Coles, P. J., & Sornborger, A. (2021) · arXiv · doi:10.48550/arxiv.2102.04313 · Cited by 28
Engineered dissipation to mitigate barren plateaus
Sannia, A., Tacchino, F., Tavernelli, I., Giorgi, G. L., & Zambrini, R. (2024) · npj Quantum Information · doi:10.1038/s41534-024-00875-0 · Cited by 38
Hamiltonian Operator Approximation for Energy Measurement and Ground-State Preparation
Bespalova, T. A., & Kyriienko, O. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.030318 · Cited by 43
Variational quantum linear solver with a dynamic ansatz
Patil, H. P., Wang, Y., & Krstić, P. (2022) · Physical Review A · doi:10.1103/physreva.105.012423 · Cited by 33
Kashif, M., Rashid, M., Al-Kuwari, S. M., & Shafique, M. (2024) · Design, Automation, and Test in Europe · doi:10.23919/date58400.2024.10546644 · Cited by 27
Entanglement entropy production in Quantum Neural Networks
Ballarin, M., Mangini, S., Montangero, S., Macchiavello, C., & Mengoni, R. (2023) · Quantum · doi:10.22331/q-2023-05-31-1023 · Cited by 35
An Evaluation of Hardware-Efficient Quantum Neural Networks for Image Data Classification
Nguyen, T., Paik, I., Watanobe, Y., & Thang, T. C. (2022) · Electronics · doi:10.3390/electronics11030437 · Cited by 34
Uncovering instabilities in variational-quantum deep Q-networks
Franz, M., Wolf, L., Periyasamy, M., Ufrecht, C., Scherer, D. D., Plinge, A., Mutschler, C., & Mauerer, W. (2023) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2022.08.021 · Cited by 26
Warm-Starting and Quantum Computing: A Systematic Mapping Study
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The barren plateaus of quantum neural networks: review, taxonomy and trends
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Learning Shallow Quantum Circuits
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Self-citationOn Depth, Robustness and Performance Using the Data Re-Uploading Single-Qubit Classifier
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Metadata
- Authors
- Skolik, A., McClean, J. R., Mohseni, M., van der Smagt, P., & Leib, M.
- Affiliations
- Leiden University (NL)
- Google (United States) (US)
- Corresponding author
- Skolik, Andrea
- Venue
- Quantum Machine Intelligence
- Published
- 2021-01-25
- Volume
- 3
- Issue
- 1
- ISSN
- 2524-4906 (ISSN-L)
- 2524-4914
- OpenAlex
- W3004252283
- Cited by
- 324
- References
- 63
- Citations by year
- 2026: 43 · 2025: 58 · 2024: 65 · 2023: 59 · 2022: 46 · 2021: 48
- FWCI
- 19.09
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Locations
- Quantum Machine Intelligence (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Bulletin of the American Physical Society
- Funders
- Horizon 2020 (828826)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Keywords
- quantum neural networks, variational quantum circuits, barren plateaus, NISQ devices, circuit depth, sampling noise, image classification, handwritten digits, generalization error
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