arXiv:2012.12658 · Physical Review Research

Entanglement devised barren plateau mitigation

Taylor L. Patti, Khadijeh Najafi, Xun Gao, Susanne F. Yelin

Published Jul 23, 2021• 167 citations

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.

DOI: 10.1103/physrevresearch.3.033090

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