Quantum neural networks are expected to be a promising application in near-term quantum computation, 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, distributed quantum neural networks have been proposed to make a prediction by approximating a large circuit with 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 multi-class classifications of handwritten digit datasets. Especially for the MNIST dataset, we succeeded in ten class classifications of the dataset 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 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：量子神经网络被认为是在近期量子计算中具有前景的应用，但面临优化过程中梯度消失以及因量子比特数量有限和浅层电路导致的表达能力受限等挑战。为缓解这些问题，研究者提出了分布式量子神经网络，通过用多个小型电路近似大型电路进行预测。然而，近似大型电路需要指数数量的小型电路评估。在此，我们提出另一种方案：将分区特征分布到多个小型量子神经网络中，并通过整合其期望值生成预测。为验证分布式方法的有效性，我们在手写数字数据集上进行了多类分类实验。特别是在MNIST数据集上，我们成功实现了十类分类，准确率超过96%。与单一量子神经网络相比，所提方法不仅在大规模数据集上实现了高精度预测，还降低了对每个量子神经网络的硬件要求。研究结果表明，分布式量子神经网络是适用于近期量子设备的实用量子机器学习算法的重要方向。我们希望该方法能为量子机器学习应用探索提供参考。