Quantifying scrambling in quantum neural networks

TL;DR

This paper links the error and trainability of quantum neural networks to their scrambling properties, using out-of-time-ordered correlators to quantify quantum chaos and its impact on training efficiency.

Contribution

It introduces a method to bound training loss and gradients in quantum neural networks using out-of-time-ordered correlators, connecting quantum chaos to network trainability.

Findings

Training loss can be bounded by out-of-time-ordered correlators.

Gradients of loss functions are governed by the network's scrambling properties.

Quantum chaos influences the trainability of quantum neural networks.

Abstract

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.