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In this work, we introduce a training framework that reduces this cost to logarithmic in the number of qubits, making gradient-based QNN optimisation feasible on near-term hardware at increasing scales.\n  Our framework combines three co-designed ingredients: (i) a structured, subspace-preserving Butterfly circuit architecture with $O(n \\log n)$ parameters and logarithmic depth; (ii) a layer-wise training strategy that confines on-hardware optimisation to one small, well-structured layer at a time; and (iii) a parallelised parameter-shift rule that exploits the commuting structure within each Butterfly layer","title":"Scalable On-Hardware Training of Quantum Neural Networks and Application to Clinical Data Imputation","url":"https://arxiv.org/abs/2606.03517","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.03517v1 Announce Type: cross \nAbstract: Training quantum neural networks (QNNs) on quantum hardware is currently bottlenecked by the cost of gradient estimation: standard parameter-shift methods require a number of circuit evaluations that grows quadratically with the number of trainable parameters, making hardware-based optimisation impractical beyond small system sizes. 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