There has been a rapid advancement in developing computational models originating from the governing principles of quantum mechanics. Quantum computing approaches such as variational quantum algorithms (VQAs) and quantum-inspired algorithms have shown advantages across various applications. VQAs have been widely used as hybrid classical-quantum computational frameworks that are well-suited for NISQ advantages. Alternatively, the quantum-inspired evolutionary algorithm (QiEA) provides an efficient search space and parameter optimization solution, useful in handling problems that consist of large parameters. Following the recent trends, quantum-inspired technique, developments, limitations, and future scope are highlighted. Also, an approach towards advancing neuromorphic computation is discussed. Neuromorphic computation and systems are a fast developing domain inherited from fast and massively parallel processing, low energy consumption, high density of millions of neurons in a chip, and have found successful applications across spatio-temporal domain areas including brain data modelling. However, they require a fast and efficient parameter optimization process in large parameter space. Finally, future directions for the development of quantum-enhanced spiking neural networks and neuromorphic systems are outlined.