Title: Achieving Scalable On-Hardware Training for Quantum Neural Networks and Its Application in Clinical Data Imputation

Abstract:

Currently, the implementation of quantum neural network (QNN) training on physical quantum devices is hindered by the high expense associated with gradient estimation. Traditional parameter-shift techniques demand a volume of circuit evaluations that scales quadratically alongside the count of trainable parameters, thereby rendering hardware-based optimization unfeasible for systems larger than a modest size. This study presents a novel training framework that lowers this computational burden to a logarithmic scale relative to the number of qubits. Consequently, gradient-driven optimization of QNNs becomes viable on near-term quantum hardware as system sizes expand.

The proposed framework integrates three co-designed components: (i) a Butterfly circuit architecture that preserves subspace structure, featuring $O(n \log n)$ parameters and logarithmic depth; (ii) a layer-wise optimization approach that restricts on-hardware tuning to individual, well-structured layers sequentially; and (iii) a parallelized parameter-shift rule. This rule leverages the commuting properties inherent within each Butterfly layer to derive all necessary gradients in a fixed number of circuit executions. Collectively, these innovations decrease the requirement for distinct circuit evaluations per optimization step from $O(n^2)$ to $O(\log n)$.

To validate this approach, we applied the framework to clinical data imputation tasks using the MIMIC-III electronic health record dataset, a rigorous benchmark known for its sensitivity to model variance and optimization instability. We trained hybrid classical-quantum models directly on IonQ Forte Enterprise trapped-ion hardware, which comprises 16 qubits. These models maintained performance parity with both ideal simulations and noisy simulations, as well as tensor-network simulations conducted at 32 qubits. Furthermore, inference for the 32-qubit models was performed on actual hardware. The resulting models achieved performance levels equal to or superior to robust classical neural network baselines in predicting patient survival outcomes. Additionally, they demonstrated lower variance across multiple runs, confirming that the suggested framework facilitates practical and scalable QNN training even under the constraints of realistic hardware environments.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC