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.

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Cited by in corpus (11)

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• Imaginary components of out-of-time correlators and information scrambling for navigating the learning landscape of a quantum machine learning model
• Quantum Information Scrambling in Quantum Many-body Scarred Systems
• Barren plateaus from learning scramblers with local cost functions
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• Information scrambling in quantum walks: Discrete-time formulation of Krylov complexity
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