Theory of overparametrization in quantum neural networks – Nature.com

Mohri, M., Rostamizadeh, A. & Talwalkar, A. Foundations of Machine Learning (MIT Press, 2018).

Vamathevan, J. et al. Applications of machine learning in drug discovery and development. Nat. Rev. Drug Discov. 18, 463477 (2019).

Article Google Scholar

Schmidt, J., Marques, M. R., Botti, S. & Marques, M. A. Recent advances and applications of machine learning in solid-state materials science. npj Comput. Mater. 5, 83 (2019).

Article Google Scholar

Blum, A. L. & Rivest, R. L. Training a 3-node neural network is NP-complete. Neural Netw. 5, 117127 (1992).

Article Google Scholar

Neyshabur, B., Li, Z., Bhojanapalli, S., LeCun, Y., & Srebro, N. Towards understanding the role of over-parametrization in generalization of neural networks. Preprint at arXiv https://doi.org/10.48550/arXiv.1805.12076 (2018).

Zhang, C., Bengio, S., Hardt, M., Recht, B. & Vinyals, O. Understanding deep learning (still) requires rethinking generalization. Commun. ACM 64, 107115 (2021).

Article Google Scholar

Allen-Zhu, Z., Li, Y. & Song, Z. A convergence theory for deep learning via over-parameterization. In Proceedings of the 36th International Conference on Machine Learning 242252 (PMLR, 2019).

Du, S. S., Zhai, X., Poczos, B., & Singh, A. Gradient descent provably optimizes over-parameterized neural networks. Preprint at arXiv https://doi.org/10.48550/arXiv.1810.02054 (2018).

Preskill, J. Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018).

Article Google Scholar

Cerezo, M. et al. Variational quantum algorithms. Nat. Rev. Phys. 3, 625644 (2021).

Article Google Scholar

Bharti, K. et al. Noisy intermediate-scale quantum algorithms. Rev. Mod. Phys. 94, 015004 (2022).

Article MathSciNet Google Scholar

Huang, H.-Y. et al. Power of data in quantum machine learning. Nat. Commun. 12, 2631 (2021).

Article Google Scholar

Abbas, A. et al. The power of quantum neural networks. Nat. Comput. Sci. 1, 403409 (2021).

Article Google Scholar

Bittel, L. & Kliesch, M. Training variational quantum algorithms is NP-hard. Phys. Rev. Lett. 127, 120502 (2021).

Article MathSciNet Google Scholar

Wierichs, D., Gogolin, C. & Kastoryano, M. Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer. Phys. Rev. Res. 2, 043246 (2020).

Article Google Scholar

Anschuetz, E. R. Critical points in quantum generative models. Preprint at arXiv https://doi.org/10.48550/arXiv.2109.06957 (2021).

McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R. & Neven, H. Barren plateaus in quantum neural network training landscapes. Nat. Commun. 9, 4812 (2018).

Article Google Scholar

Cerezo, M., Sone, A., Volkoff, T., Cincio, L. & Coles, P. J. Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nat. Commun. 12, 1791 (2021).

Article Google Scholar

Wang, S. et al. Noise-induced barren plateaus in variational quantum algorithms. Nat. Commun. 12, 6961 (2021).

Article Google Scholar

Stilck Frana, D. & Garcia-Patron, R. Limitations of optimization algorithms on noisy quantum devices. Nat. Phys. 17, 12211227 (2021).

Article Google Scholar

Wiersema, R. et al. Exploring entanglement and optimization within the Hamiltonian variational ansatz. PRX Quantum 1, 020319 (2020).

Article Google Scholar

Kiani, B. T., Lloyd, S. & Maity, R. Learning unitaries by gradient descent. Preprint at arXiv https://doi.org/10.48550/arXiv.2001.11897 (2020).

Funcke, L. et al. Best-approximation error for parametric quantum circuits. In 2021 IEEE International Conference on Web Services (ICWS) 693702 (IEEE, 2021).

Lee, J., Magann, A. B., Rabitz, H. A. & Arenz, C. Progress toward favorable landscapes in quantum combinatorial optimization. Phys. Rev. A 104, 032401 (2021).

Article MathSciNet Google Scholar

Zeier, R. & Schulte-Herbrggen, T. Symmetry principles in quantum systems theory. J. Math. Phys. 52, 113510 (2011).

Article MathSciNet MATH Google Scholar

Meyer, J. J. Fisher information in noisy intermediate-scale quantum applications. Quantum 5, 539 (2021).

Article Google Scholar

Moore, K. W. & Rabitz, H. Exploring constrained quantum control landscapes. J. Chem. Phys. 137, 134113 (2012).

Article Google Scholar

Larocca, M., Calzetta, E. & Wisniacki, D. A. Exploiting landscape geometry to enhance quantum optimal control. Phys. Rev. A 101, 023410 (2020).

Article MathSciNet Google Scholar

Wu, R.-B., Long, R., Dominy, J., Ho, T.-S. & Rabitz, H. Singularities of quantum control landscapes. Phys. Rev. A 86, 013405 (2012).

Article Google Scholar

Rach, N., Mller, M. M., Calarco, T. & Montangero, S. Dressing the chopped-random-basis optimization: a bandwidth-limited access to the trap-free landscape. Phys. Rev. A 92, 062343 (2015).

Article Google Scholar

Larocca, M., Poggi, P. M. & Wisniacki, D. A. Quantum control landscape for a two-level system near the quantum speed limit. J. Phys. A Math. Theor. 51, 385305 (2018).

Article MathSciNet MATH Google Scholar

Larocca, M. et al. Diagnosing barren plateaus with tools from quantum optimal control. Quantum 6, 824 (2022).

Article Google Scholar

Haug, T., Bharti, K. & Kim, M. S. Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021).

Article Google Scholar

Larocca, M., Calzetta, E. & Wisniacki, D. Fourier compression: a customization method for quantum control protocols. Phys. Rev. A 102, 033108 (2020).

Article Google Scholar

Efthymiou, S. et al. Qibo: a framework for quantum simulation with hardware acceleration. Quantum Sci. Technol. 7, 015018 (2021).

Article Google Scholar

Peruzzo, A. et al. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 5, 4213 (2014).

Article Google Scholar

Garca-Martn, D., Larocca, M. & Cerezo, M. Effects of noise on the overparametrization of quantum neural networks. Preprint at arXiv https://doi.org/10.48550/arXiv.2302.05059 (2023).

Fukumizu, K. A regularity condition of the information matrix of a multilayer perceptron network. Neural Netw. 9, 871879 (1996).

Article Google Scholar

Chan, N. & Kwong, M. K. Hermitian matrix inequalities and a conjecture. Am. Math. Monthly 92, 533541 (1985).

Article MathSciNet MATH Google Scholar

Glaser, S. J. et al. Training Schrdingers cat: quantum optimal control. Eur. Phys. J. D 69, 279 (2015).

Article Google Scholar

Rembold, P. et al. Introduction to quantum optimal control for quantum sensing with nitrogen-vacancy centers in diamond. AVS Quantum Sci. 2, 024701 (2020).

Article Google Scholar

Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator. Nature 595, 227232 (2021).

Article Google Scholar

Magann, A. B., Rudinger, K. M., Grace, M. D. & Sarovar, M. Feedback-based quantum optimization. Phys. Rev. Lett. 129, 250502 (2022).

Article Google Scholar

Magann, A. B. et al. From pulses to circuits and back again: a quantum optimal control perspective on variational quantum algorithms. PRX Quantum 2, 010101 (2021).

Article Google Scholar

Hsieh, M., Wu, R. & Rabitz, H. Topology of the quantum control landscape for observables. J. Chem. Phys. 130, 104109 (2009).

Article Google Scholar

Ho, T.-S., Dominy, J. & Rabitz, H. Landscape of unitary transformations in controlled quantum dynamics. Phys. Rev. A 79, 013422 (2009).

Article MathSciNet Google Scholar

Riviello, G. et al. Searching for quantum optimal control fields in the presence of singular critical points. Phys. Rev. A 90, 013404 (2014).

Article Google Scholar

Schatzki, L., Arrasmith, A., Coles, P. J. & Cerezo, M. Entangled datasets for quantum machine learning. Preprint at arXiv https://doi.org/10.48550/arXiv.2109.03400 (2021).

Garca-Martn, D. DiegoGM91/theory-of-overparametrization: v0.0.1. Zenodo https://doi.org/10.5281/zenodo.7916659 (2023).

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