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  • Open Access

Entanglement devised barren plateau mitigation

Taylor L. Patti1,*, Khadijeh Najafi2, Xun Gao1, and Susanne F. Yelin1

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
  • 2Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA; IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, New York 10598 USA; and Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, California 91125, USA

  • *taylorpatti@g.harvard.edu
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Phys. Rev. Research 3, 033090 – Published 23 July, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.033090

Abstract

Hybrid quantum-classical variational algorithms are one of the most propitious implementations of quantum computing on near-term devices, offering classical machine-learning support to quantum scale solution spaces. However, numerous studies have demonstrated that the rate at which this space grows in qubit number could preclude learning in deep quantum circuits, a phenomenon known as barren plateaus. In this work, we implicate random entanglement, i.e., entanglement that is formed due to state evolution with random unitaries, as a source of barren plateaus and characterize them in terms of many-body entanglement dynamics, detailing their formation as a function of system size, circuit depth, and circuit connectivity. Using this comprehension of entanglement, we propose and demonstrate a number of barren plateau ameliorating techniques, including initial partitioning of cost function and non-cost function registers, meta-learning of low-entanglement circuit initializations, selective inter-register interaction, entanglement regularization, the addition of Langevin noise, and rotation into preferred cost function eigenbases. We find that entanglement limiting, both automatic and engineered, is a hallmark of high-accuracy training and emphasize that, because learning is an iterative organization process whereas barren plateaus are a consequence of randomization, they are not necessarily unavoidable or inescapable. Our work forms both a theoretical characterization and a practical toolbox; first defining barren plateaus in terms of random entanglement and then employing this expertise to strategically combat them.

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Phys. Rev. Research 3, 033090– Published 23 July, 2021
  • Received 22 December 2020
  • Accepted 21 June 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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