Quantifying scrambling in quantum neural networks

We quantify the role of scrambling in quantum machine learning. We characterize a quantum neural network’s (QNNs) error in terms of the network’s scrambling properties via the out-of-time-ordered correlator (OTOC). A network can be trained by minimizing a loss function. We show that the loss function can be bounded by the OTOC. We prove that the gradient of the loss function can be bounded by the gradient of the OTOC. This demonstrates that the OTOC landscape regulates the trainability of a QNN. We show numerically that this landscape is flat for maximally scrambling QNNs, which can pose a challenge to training. Our results pave the way for the exploration of quantum chaos in quantum neural networks.