  Quantum machine learning is in a period of rapid development and discovery,
however it still lacks the resources and diversity of computational models of
its classical complement. With the growing difficulties of classical models
requiring extreme hardware and power solutions, and quantum models being
limited by noisy intermediate-scale quantum (NISQ) hardware, there is an
emerging opportunity to solve both problems together. Here we introduce a new
software model for quantum neuromorphic computing -- a quantum leaky
integrate-and-fire (QLIF) neuron, implemented as a compact high-fidelity
quantum circuit, requiring only 2 rotation gates and no CNOT gates. We use
these neurons as building blocks in the construction of a quantum spiking
neural network (QSNN), and a quantum spiking convolutional neural network
(QSCNN), as the first of their kind. We apply these models to the MNIST,
Fashion-MNIST, and KMNIST datasets for a full comparison with other classical
and quantum models. We find that the proposed models perform competitively,
with comparative accuracy, with efficient scaling and fast computation in
classical simulation as well as on quantum devices.
