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Entanglement devised barren plateau mitigation

Patti, Taylor L. and Najafi, Khadijeh and Gao, Xun and Yelin, Susanne F. (2021) Entanglement devised barren plateau mitigation. Physical Review Research, 3 (3). Art. No. 033090. ISSN 2643-1564. doi:10.1103/physrevresearch.3.033090.

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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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Patti, Taylor L.0000-0002-4242-6072
Additional Information:© 2021 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. Received 22 December 2020; accepted 21 June 2021; published 23 July 2021. S.F.Y. and T.L.P. would like to thank the AFOSR and the NSF for funding through the CUA-PFC grant. T.L.P. acknowledges that this material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1745303. X.G. is supported by the Postdoctoral Fellowship in Quantum Science of the Harvard-MPQ Center for Quantum Optics, the Templeton Religion Trust grant TRT 0159, and by the Army Research Office under Grant W911NF1910302 and MURI Grant W911NF-20-1-0082.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
NSF Graduate Research FellowshipDGE-1745303
Harvard UniversityUNSPECIFIED
John Templeton FoundationTRT 0159
Army Research Office (ARO)W911NF1910302
Army Research Office (ARO)W911NF-20-1-0082
Issue or Number:3
Record Number:CaltechAUTHORS:20210820-000335093
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110317
Deposited By: Tony Diaz
Deposited On:20 Aug 2021 16:09
Last Modified:20 Aug 2021 16:09

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