Fault-tolerant quantum neural networks suppressing barren plateaus via localised cost functions and shallow parametrised architectures

The barren plateau phenomenon, marked by exponentially vanishing gradients in variational quantum algorithms, poses a critical obstacle in training quantum neural networks (QNNs) at scale. While error mitigation and shallow architectures partially address this issue in noisy intermediate-scale quantum (NISQ) devices, the potential of fault-tolerant quantum computing to restore trainability has remained largely unexplored. Here, we analytically demonstrate that fault-tolerant QNNs (FT-QNNs) , when co-designed with locality-preserving parametrised circuits and localised cost functions, suppress both noise-induced and expressibility-induced barren plateaus. By deriving lower bounds on gradient variance, we show that such architectures enable polynomial scaling of gradients with system size, paving the way for efficient optimisation. These findings highlight a paradigm shift: fault tolerance must be integrated with ansatz and cost-function design to realise scalable quantum machine learning beyond the NISQ era.