Quantifying scrambling in 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.

References in corpus (4)

• Black holes as mirrors: quantum information in random subsystems
• Slow scrambling in disordered quantum systems
• Simulating a perceptron on a quantum computer
• Chaos and Complexity from Quantum Neural Network: A study with Diffusion Metric in Machine Learning

Cited by in corpus (1)

• Quantum Information Scrambling in Quantum Many-body Scarred Systems