Quantum neural networks are expected to be a promising application in near-term quantum computing, but face challenges such as vanishing gradients during optimization and limited expressibility by a limited number of qubits and shallow circuits. To mitigate these challenges, an approach using distributed quantum neural networks has been proposed to make a prediction by approximating outputs of a large circuit using multiple small circuits. However, the approximation of a large circuit requires an exponential number of small circuit evaluations. Here, we instead propose to distribute partitioned features over multiple small quantum neural networks and use the ensemble of their expectation values to generate predictions. To verify our distributed approach, we demonstrate ten class classification of the Semeion and MNIST handwritten digit datasets. The results of the Semeion dataset imply that while our distributed approach may outperform a single quantum neural network in classification performance, excessive partitioning reduces performance. Nevertheless, for the MNIST dataset, we succeeded in ten class classification with exceeding 96\% accuracy. Our proposed method not only achieved highly accurate predictions for a large dataset but also reduced the hardware requirements for each quantum neural network compared to a large single quantum neural network. Our results highlight distributed quantum neural networks as a promising direction for practical quantum machine learning algorithms compatible with near-term quantum devices. We hope that our approach is useful for exploring quantum machine learning applications.

翻译：量子神经网络有望成为近期量子计算中的一项有前景的应用，但面临着优化过程中梯度消失以及受限于少量量子比特和浅层电路导致的表达能力受限等挑战。为缓解这些挑战，已有研究提出采用分布式量子神经网络的方法，通过利用多个小电路近似大电路的输出来进行预测。然而，近似一个大电路需要对指数数量的小电路进行评估。在此，我们转而提出将分块特征分布到多个小型量子神经网络上，并利用其期望值的集成来生成预测。为验证我们的分布式方法，我们演示了对Semeion和MNIST手写数字数据集的十类分类。Semeion数据集的结果表明，尽管我们的分布式方法在分类性能上可能优于单个量子神经网络，但过度分块会降低性能。尽管如此，对于MNIST数据集，我们成功实现了准确率超过96%的十类分类。我们提出的方法不仅对大型数据集实现了高精度预测，而且与单个大型量子神经网络相比，降低了对每个量子神经网络的硬件要求。我们的研究结果凸显了分布式量子神经网络作为与近期量子设备兼容的实际量子机器学习算法的一个有前景的方向。我们希望我们的方法能有助于探索量子机器学习应用。