We characterize a quantum neural network's error in terms of the network's scrambling properties via the out-of-time-ordered correlator. A network can be trained by optimizing either a loss function or a cost function. We show that, with some probability, both functions can be bounded by out-of-time-ordered correlators. The gradients of these functions can be bounded by the gradient of the out-of-time-ordered correlator, demonstrating that the network's scrambling ability governs its trainability. Our results pave the way for the exploration of quantum chaos in quantum neural networks.
@article{arxiv.2112.01440,
title = {Quantifying scrambling in quantum neural networks},
author = {Roy J. Garcia and Kaifeng Bu and Arthur Jaffe},
journal= {arXiv preprint arXiv:2112.01440},
year = {2022}
}