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Bulletin of the American Physical Society

Quantum algorithms for optimisation problems in machine learning

Maria Schuld, Patrick Rebentrost, Seth Lloyd, Ilya Sinayskiy, Francesco Petruccione

Published Mar 16, 2017• 0 citations
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This study focuses on the integration of quantum computing and artificial intelligence, proposing a multi-task optimisation framework based on the quantum annealing algorithm to address the bottlenecks in computational efficiency and model optimisation in traditional machine learning. The study converts problems such as time series prediction, Support Vector Machine (SVM) classification, and Convolutional Neural Network (CNN) training into Quadratic Unconstrained Binary Optimisation (QUBO) models and achieves parameter optimisation through the simulated annealing algorithm. In time series prediction, an autoregressive model is constructed based on historical data. The problem of minimising prediction error is mapped to a binary optimisation problem through QUBO transformation, and the model parameters are solved using the simulated annealing algorithm to achieve trend prediction of the target variable, validating the effectiveness of quantum optimisation in time series analysis. For classification tasks, the hinge loss and regularisation terms of SVM are converted into a QUBO matrix to optimise the classification hyperplane parameters, thereby enhancing the model's classification performance in the feature space. The results demonstrate that this method exhibits strong geometric interpretability and generalisation capabilities in binary classification problems. In the field of deep learning, L2 regularisation is introduced into the weight optimisation of CNNs, and a QUBO model is constructed to explore the application of quantum optimisation in image feature extraction and network training. Although limited by the scale of variables, this demonstrates the potential value of combining quantum computing with deep learning. The study shows that the quantum optimisation framework can effectively improve solution efficiency in small- to medium-scale problems, providing new technical pathways for time series analysis, classification tasks, and deep learning optimisation.