  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.
