The DOI matches its Crossref record; 61 of the 63 references it cites were found in a registry or an index.
Layerwise learning for quantum neural networks
Open accessAbstract
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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Citations
Cites
Adam: A Method for Stochastic Optimization
Kingma, D. P., & Ba, J. (2014) · arXiv · doi:10.48550/arxiv.1412.6980 · Cited by 98,946
Learning representations by back-propagating errors
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986) · Nature · doi:10.1038/323533a0 · Cited by 31,892
A fast learning algorithm for deep belief nets
Hinton, G. E., Osindero, S., & Teh, Y.-W. (2006) · Neural Computation · doi:10.1162/neco.2006.18.7.1527 · Cited by 16,336
Quantum supremacy using a programmable superconducting processor
Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J. C., Barends, R., Biswas, R., Boixo, S., Brandao, F. G. S. L., Buell, D. A., et al. (2019) · Nature · doi:10.1038/s41586-019-1666-5 · Cited by 7,720
Self-citationGreedy layer-wise training of deep networks
Bengio, Y., Lamblin, P., Popovici, D., & Larochelle, H. (2007) · Advances in Neural Information Processing Systems 19 · doi:10.7551/mitpress/7503.003.0024 · Cited by 4,841
A variational eigenvalue solver on a photonic quantum processor
Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P. J., Aspuru-Guzik, A., & O’Brien, J. L. (2014) · Nature Communications · doi:10.1038/ncomms5213 · Cited by 4,552
Self-citationHardware-efficient variational quantum eigensolver for small molecules and quantum magnets
Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J. M., & Gambetta, J. M. (2017) · Nature · doi:10.1038/nature23879 · Cited by 2,982
Supervised learning with quantum-enhanced feature spaces
Havlíček, V., Córcoles, A. D., Temme, K., Harrow, A. W., Kandala, A., Chow, J. M., & Gambetta, J. M. (2019) · Nature · doi:10.1038/s41586-019-0980-2 · Cited by 2,572
The Cascade-Correlation learning architecture
Fahlman, S. E., & Lebiere, C. J. (2018) · doi:10.1184/r1/6610403 · Cited by 2,391
Barren plateaus in quantum neural network training landscapes
McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R., & Neven, H. (2018) · Nature Communications · doi:10.1038/s41467-018-07090-4 · Cited by 2,329
Self-citation
Research works printed but not linked: 6
- Cerezo M, Sone A, Volkoff T, Cincio L, Coles PJ (2020) arXiv:2001.00550 · arXiv
- Chen H, Wossnig L, Severini S, Neven H, Mohseni M (2018) arXiv:1805.08654 · arXiv
- Fahlman S E, Lebiere C (1990) Adv Neural Inf Process 2:524–532. https://doi.org/10.1.1.125.6421
- Hettinger C, Christensen T, Ehlert B, Humpherys J, Jarvis T, Wade S (2017) In: 31st Conference on Neural Information Processing Systems. 1706.02480
- Volkoff T, Coles PJ (2020) arXiv:2005.12200 · arXiv
- Yung M-H, Casanova J, Mezzacapo A, McClean J, Lamata L, Aspuru-Guzik A, Solano E (2014) Sci Rep 4(3589):1–7. https://www.nature.com/articles/srep03589
Cited by
Sorted by citations
Variational quantum algorithms
Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S. C., Endo, S., Fujii, K., McClean, J. R., Mitarai, K., Yuan, X., Cincio, L., et al. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00348-9 · Cited by 3,385
“[178] introduced a method where one employs layerby-layer training.”
MethodSelf-citationNoisy intermediate-scale quantum algorithms
Bharti, K., Cervera-Lierta, A., Kyaw, T. H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J. S., Menke, T., et al. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.015004 · Cited by 2,231
The power of quantum neural networks
Abbas, A., Sutter, D., Zoufal, C., Lucchi, A., Figalli, A., & Woerner, S. (2021) · Nature Computational Science · doi:10.1038/s43588-021-00084-1 · Cited by 1,082
Cost function dependent barren plateaus in shallow parametrized quantum circuits
Cerezo, M., Sone, A., Volkoff, T., Cincio, L., & Coles, P. J. (2021) · Nature Communications · doi:10.1038/s41467-021-21728-w · Cited by 1,047
The Variational Quantum Eigensolver: A review of methods and best practices
Tilly, J., Chen, H., Cao, S., Picozzi, D., Setia, K., Li, Y., Grant, E., Wossnig, L., Rungger, I., Booth, G. H., et al. (2022) · Physics Reports · doi:10.1016/j.physrep.2022.08.003 · Cited by 1,031
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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