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2020

Higher Order Derivatives of Quantum Neural Networks with Barren Plateaus

Cerezo, M., Coles, Patrick J.

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Quantum neural networks (QNNs) offer a powerful paradigm for programming near-term quantum computers and have the potential to speedup applications ranging from data science to chemistry to materials science.

However, a possible obstacle to realizing that speedup is the Barren Plateau (BP) phenomenon, whereby the gradient vanishes exponentially in the system size $n$ for certain QNN architectures.
The question of whether high-order derivative information such as the Hessian could help escape a BP was recently posed in the literature.
Here we show that the elements of the Hessian are exponentially suppressed in a BP, so estimating the Hessian in this situation would require a precision that scales exponentially with $n$.

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