Exploring quantum neural networks for binary classification on MNIST dataset: A swap test approach.

In this study, we propose a novel modularized Quantum Neural Network (mQNN) model tailored to address the binary classification problem on the MNIST dataset. The mQNN organizes input information using quantum images and trainable quantum parameters encoded in superposition states. Leveraging quantum parallelism, the model efficiently processes inner product calculations of quantum neurons via the swap test, achieving constant complexity. To enhance the expressive capacity of the mQNN, nonlinear transformations, specifically quantum versions of activation functions, are integrated into the quantum network. The mQNN's circuits are constructed from flexible quantum modules, allowing the model to adapt its structure based on varying input data types and scales for optimal performance. Furthermore, rigorous mathematical derivations are employed to validate the quantum state evolution during computation within a quantum neuron. Testing on the Pennylane platform simulates the quantum environment and confirms the mQNN's effectiveness on the MNIST dataset. These findings highlight the potential of quantum computing in advancing image classification tasks.