Quantum Kernel SVM for Image Classification using PennyLane on Fashion-MNIST Dataset

Abstract

Quantum Machine Learning (QML) combines quantum computing principles and traditional machine learning principles to provide new ways to solve difficult classification problems through the use of quantum technology. The goal of this paper is to implement a Quantum Kernel Support Vector Machine (QKSVM) using PennyLane and evaluate it against a standard image classification dataset, Fashion-MNIST. The Fashion-MNIST images are represented as 28x28 grayscale pixel arrays; they are normalized using a min-max normalizer with output values between zero and one. The 28x28 arrays are then dimensionally reduced to a size of four principal components (approximately 85% cumulative explained variance), and the QKSVM will utilize a quantum circuit limited to four qubits which is consistent with today's Noisy, Intermediate-Scale Quantum (NISQ) capabilities for performing simulations. Each input feature is represented as a qubit via an RY rotation and the qubits are then entangled using a CNOT circuit to generate the quantum kernel matrix, which is computed as the pairwise fidelity of each input image's state, which is subsequently used by a classical SVM classifier implementing a one-versus-all classification method. The QKSVM achieved approximately 40% accuracy and a macro-F1 score of 0.37 on a 100 sample stratified subset of the Fashion-MNIST test dataset, compared with 60% and 91.2%, respectively, using a classical Radial Basis Function Support Vector Machine (RBF-SVM) classifier with the same four principal components of input features and a Convolutional Neural Network (CNN) with full input images. With a primary bottleneck of qubit count, circuit depth, and shot noise, this work serves as a fully documented and reproducible baseline for future research on quantifying the performance of hybrid classical and quantum image classifiers across standardized image dataset benchmarks.