An Efficient Hybrid Quantum Variational Classifier With Matrix Product State

Matrix Product States have been extensively explored as a powerful tool for simulating quantum states in image classification task. However, most research has focused on classical simulations or computations involving high-dimensional unitaries, and significant challenges still exist in the practical preparation of Matrix Product States on quantum computers. This paper proposes a novel and practically feasible quantum variational algorithm based on Matrix Product States for image classification task. We design a hardware-efficient quantum circuit with several adjustable entangling operators to prepare the local tensors in Matrix Product States and integrate minimal residuals to ensure computational stability. We demonstrate that our algorithm can reduce the parameter complexity from growing exponentially with the system size to a linear scale. To validate the effectiveness of this quantum variational algorithm, we conducted experiments on the MNIST dataset, achieving accuracies of 99.95% and 95.96% for binary and ten-class classification tasks, which outperforms other related quantum algorithms. This work advances the practical application of quantum machine learning in resource-constrained environments of quantum computing.