An initialization strategy for addressing barren plateaus in parametrized quantum circuits

Edward Grant1, Leonard Wossnig1, Mateusz Ostaszewski2, and Marcello Benedetti3

1Rahko Limited & Department of Computer Science, University College London
2Institute of Theoretical and Applied Informatics, Polish Academy of Sciences
3Cambridge Quantum Computing Limited & Department of Computer Science, University College London

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Abstract

Parametrized quantum circuits initialized with random initial parameter values are characterized by barren plateaus where the gradient becomes exponentially small in the number of qubits. In this technical note we theoretically motivate and empirically validate an initialization strategy which can resolve the barren plateau problem for practical applications. The technique involves randomly selecting some of the initial parameter values, then choosing the remaining values so that the circuit is a sequence of shallow blocks that each evaluates to the identity. This initialization limits the effective depth of the circuits used to calculate the first parameter update so that they cannot be stuck in a barren plateau at the start of training. In turn, this makes some of the most compact ansätze usable in practice, which was not possible before even for rather basic problems. We show empirically that variational quantum eigensolvers and quantum neural networks initialized using this strategy can be trained using a gradient based method.

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[1] Jarrod R McClean, Sergio Boixo, Vadim N Smelyanskiy, Ryan Babbush, and Hartmut Neven. Barren plateaus in quantum neural network training landscapes. Nature communications, 9(1):4812, 2018. https:/​/​doi.org/​10.1038/​s41467-018-07090-4.
https:/​/​doi.org/​10.1038/​s41467-018-07090-4

[2] Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, and Jeremy L O’brien. A variational eigenvalue solver on a photonic quantum processor. Nature communications, 5:4213, 2014. https:/​/​doi.org/​10.1038/​ncomms5213.
https:/​/​doi.org/​10.1038/​ncomms5213

[3] Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M Chow, and Jay M Gambetta. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549(7671):242, 2017. https:/​/​doi.org/​10.1038/​nature23879.
https:/​/​doi.org/​10.1038/​nature23879

[4] Maria Schuld, Alex Bocharov, Krysta Svore, and Nathan Wiebe. Circuit-centric quantum classifiers. arXiv preprint arXiv:1804.00633, 2018.
arXiv:1804.00633

[5] Edward Grant, Marcello Benedetti, Shuxiang Cao, Andrew Hallam, Joshua Lockhart, Vid Stojevic, Andrew G Green, and Simone Severini. Hierarchical quantum classifiers. npj Quantum Information, 4(1):65, 2018. https:/​/​doi.org/​10.1038/​s41534-018-0116-9.
https:/​/​doi.org/​10.1038/​s41534-018-0116-9

[6] Hongxiang Chen, Leonard Wossnig, Simone Severini, Hartmut Neven, and Masoud Mohseni. Universal discriminative quantum neural networks. arXiv preprint arXiv:1805.08654, 2018.
arXiv:1805.08654

[7] Dominic Verdon. Unitary 2-designs, variational quantum eigensolvers, and barren plateaus. https:/​/​qitheory.blogs.bristol.ac.uk/​files/​2019/​02/​barrenplateausblogpost-1xqcazi.pdf, 2019. [Online; accessed 13-March-2019].
https:/​/​qitheory.blogs.bristol.ac.uk/​files/​2019/​02/​barrenplateausblogpost-1xqcazi.pdf

[8] Zbigniew Puchała and Jaroslaw Adam Miszczak. Symbolic integration with respect to the haar measure on the unitary groups. Bulletin of the Polish Academy of Sciences Technical Sciences, 65(1):21–27, 2017. https:/​/​doi.org/​10.1515/​bpasts-2017-0003.
https:/​/​doi.org/​10.1515/​bpasts-2017-0003

[9] Andris Ambainis and Joseph Emerson. Quantum t-designs: t-wise independence in the quantum world. In Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07), pages 129–140. IEEE, 2007. https:/​/​doi.org/​10.1109/​CCC.2007.26.
https:/​/​doi.org/​10.1109/​CCC.2007.26

[10] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
arXiv:1412.6980

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[4] Iordanis Kerenidis and Alessandro Luongo, "Classification of the MNIST data set with quantum slow feature analysis", Physical Review A 101 6, 062327 (2020).

[5] Cristina Cîrstoiu, Zoë Holmes, Joseph Iosue, Lukasz Cincio, Patrick J. Coles, and Andrew Sornborger, "Variational fast forwarding for quantum simulation beyond the coherence time", npj Quantum Information 6 1, 82 (2020).

[6] Ryan LaRose, Arkin Tikku, Étude O’Neel-Judy, Lukasz Cincio, and Patrick J. Coles, "Variational quantum state diagonalization", arXiv:1810.10506, npj Quantum Information 5 1, 57 (2019).

[7] Kathleen E. Hamilton, Catherine D. Schuman, Steven R. Young, Ryan S. Bennink, Neena Imam, and Travis S. Humble, "Accelerating Scientific Computing in the Post-Moore’s Era", ACM Transactions on Parallel Computing 7 1, 1 (2020).

[8] Jacques Carolan, Masoud Mohseni, Jonathan P. Olson, Mihika Prabhu, Changchen Chen, Darius Bunandar, Murphy Yuezhen Niu, Nicholas C. Harris, Franco N. C. Wong, Michael Hochberg, Seth Lloyd, and Dirk Englund, "Variational quantum unsampling on a quantum photonic processor", Nature Physics 16 3, 322 (2020).

[9] Alexey Uvarov, Jacob D. Biamonte, and Dmitry Yudin, "Variational quantum eigensolver for frustrated quantum systems", Physical Review B 102 7, 075104 (2020).

[10] Sam McArdle, Suguru Endo, Alan Aspuru-Guzik, Simon Benjamin, and Xiao Yuan, "Quantum computational chemistry", arXiv:1808.10402, Reviews of Modern Physics 92 1, 015003 (2018).

[11] Mateusz Ostaszewski, Edward Grant, and Marcello Benedetti, "Quantum circuit structure learning", arXiv:1905.09692.

[12] Guillaume Verdon, Michael Broughton, Jarrod R. McClean, Kevin J. Sung, Ryan Babbush, Zhang Jiang, Hartmut Neven, and Masoud Mohseni, "Learning to learn with quantum neural networks via classical neural networks", arXiv:1907.05415.

[13] Marcello Benedetti, Erika Lloyd, Stefan Sack, and Mattia Fiorentini, "Parameterized quantum circuits as machine learning models", Quantum Science and Technology 4 4, 043001 (2019).

[14] Sukin Sim, Peter D. Johnson, and Alan Aspuru-Guzik, "Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms", arXiv:1905.10876.

[15] Max Wilson, Sam Stromswold, Filip Wudarski, Stuart Hadfield, Norm M. Tubman, and Eleanor Rieffel, "Optimizing quantum heuristics with meta-learning", arXiv:1908.03185.

[16] Arthur G. Rattew, Shaohan Hu, Marco Pistoia, Richard Chen, and Steve Wood, "A Domain-agnostic, Noise-resistant, Hardware-efficient Evolutionary Variational Quantum Eigensolver", arXiv:1910.09694.

[17] Jules Tilly, Glenn Jones, Hongxiang Chen, Leonard Wossnig, and Edward Grant, "Computation of molecular excited states on IBMQ using a Discriminative Variational Quantum Eigensolver", arXiv:2001.04941.

[18] Johannes Bausch, "Recurrent Quantum Neural Networks", arXiv:2006.14619.

The above citations are from Crossref's cited-by service (last updated successfully 2020-10-28 08:29:11) and SAO/NASA ADS (last updated successfully 2020-10-28 08:29:12). The list may be incomplete as not all publishers provide suitable and complete citation data.