  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.
