  In this research, we explore the integration of quantum computing with
classical machine learning for image classification tasks, specifically
focusing on the MNIST dataset. We propose a hybrid quantum-classical approach
that leverages the strengths of both paradigms. The process begins with
preprocessing the MNIST dataset, normalizing the pixel values, and reshaping
the images into vectors. An autoencoder compresses these 784-dimensional
vectors into a 64-dimensional latent space, effectively reducing the data's
dimensionality while preserving essential features. These compressed features
are then processed using a quantum circuit implemented on a 5-qubit system. The
quantum circuit applies rotation gates based on the feature values, followed by
Hadamard and CNOT gates to entangle the qubits, and measurements are taken to
generate quantum outcomes. These outcomes serve as input for a classical neural
network designed to classify the MNIST digits. The classical neural network
comprises multiple dense layers with batch normalization and dropout to enhance
generalization and performance. We evaluate the performance of this hybrid
model and compare it with a purely classical approach. The experimental results
indicate that while the hybrid model demonstrates the feasibility of
integrating quantum computing with classical techniques, the accuracy of the
final model, trained on quantum outcomes, is currently lower than the classical
model trained on compressed features. This research highlights the potential of
quantum computing in machine learning, though further optimization and advanced
quantum algorithms are necessary to achieve superior performance.
