  Classical Random Neural Networks (RNNs) have demonstrated effective
applications in decision making, signal processing, and image recognition
tasks. However, their implementation has been limited to deterministic digital
systems that output probability distributions in lieu of stochastic behaviors
of random spiking signals. We introduce the novel class of supervised Random
Quantum Neural Networks (RQNNs) with a robust training strategy to better
exploit the random nature of the spiking RNN. The proposed RQNN employs hybrid
classical-quantum algorithms with superposition state and amplitude encoding
features, inspired by quantum information theory and the brain's
spatial-temporal stochastic spiking property of neuron information encoding. We
have extensively validated our proposed RQNN model, relying on hybrid
classical-quantum algorithms via the PennyLane Quantum simulator with a limited
number of \emph{qubits}. Experiments on the MNIST, FashionMNIST, and KMNIST
datasets demonstrate that the proposed RQNN model achieves an average
classification accuracy of $94.9\%$. Additionally, the experimental findings
illustrate the proposed RQNN's effectiveness and resilience in noisy settings,
with enhanced image classification accuracy when compared to the classical
counterparts (RNNs), classical Spiking Neural Networks (SNNs), and the
classical convolutional neural network (AlexNet). Furthermore, the RQNN can
deal with noise, which is useful for various applications, including computer
vision in NISQ devices. The PyTorch code (https://github.com/darthsimpus/RQN)
is made available on GitHub to reproduce the results reported in this
manuscript.
