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Along with the development of AI democratization, the machine learning approach, in particular neural networks, has been applied to wide-range applications. In different application scenarios, the neural network will be accelerated on the tailored computing platform. The acceleration of neural networks on classical computing platforms, such as CPU, GPU, FPGA, ASIC, has been widely studied; however, when the scale of the application consistently grows up, the memory bottleneck becomes obvious, widely known as memory-wall. In response to such a challenge, advanced quantum computing, which can represent 2^N states with N quantum bits (qubits), is regarded as a promising solution. It is imminent to know how to design the quantum circuit for accelerating neural networks. Most recently, there are initial works studying how to map neural networks to actual quantum processors. To better understand the state-of-the-art design and inspire new design methodology, this paper carries out a case study to demonstrate an end-to-end implementation. On the neural network side, we employ the multilayer perceptron to complete image classification tasks using the standard and widely used MNIST dataset. On the quantum computing side, we target IBM Quantum processors, which can be programmed and simulated by using IBM Qiskit. This work targets the acceleration of the inference phase of a trained neural network on the quantum processor. Along with the case study, we will demonstrate the typical procedure for mapping neural networks to quantum circuits.