An initialization strategy for addressing barren plateaus in parametrized quantum circuits

Edward Grant; Leonard Wossnig; Mateusz Ostaszewski; Marcello Benedetti

doi:10.22331/q-2019-12-09-214

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

Published:	2019-12-09, volume 3, page 214
Eprint:	arXiv:1903.05076v3
Doi:	https://doi.org/10.22331/q-2019-12-09-214
Citation:	Quantum 3, 214 (2019).

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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.

► BibTeX data

@article{Grant2019initialization,
  doi = {10.22331/q-2019-12-09-214},
  url = {https://doi.org/10.22331/q-2019-12-09-214},
  title = {An initialization strategy for addressing barren plateaus in parametrized quantum circuits},
  author = {Grant, Edward and Wossnig, Leonard and Ostaszewski, Mateusz and Benedetti, Marcello},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {3},
  pages = {214},
  month = dec,
  year = {2019}
}

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