In recent years, the development of quantum annealers has enabled experimental demonstrations and has increased research interest in applications of quantum annealing, such as in quantum machine learning and in particular for the popular quantum SVM. Several versions of the quantum SVM have been proposed, and quantum annealing has been shown to be effective in them. Extensions to multiclass problems have also been made, which consist of an ensemble of multiple binary classifiers. This work proposes a novel quantum SVM formulation for direct multiclass classification based on quantum annealing, called Quantum Multiclass SVM (QMSVM). The multiclass classification problem is formulated as a single Quadratic Unconstrained Binary Optimization (QUBO) problem solved with quantum annealing. The main objective of this work is to evaluate the feasibility, accuracy, and time performance of this approach. Experiments have been performed on the D-Wave Advantage quantum annealer for a classification problem on remote sensing data. The results indicate that, despite the memory demands of the quantum annealer, QMSVM can achieve accuracy that is comparable to standard SVM methods and, more importantly, it scales much more efficiently with the number of training examples, resulting in nearly constant time. This work shows an approach for bringing together classical and quantum computation, solving practical problems in remote sensing with current hardware.

翻译：近年来，量子退火器的发展推动了实验验证，并激发了人们对量子退火应用的研究兴趣，例如量子机器学习，尤其是广受欢迎的量子支持向量机。目前已提出多种量子支持向量机版本，并证实了量子退火在其应用中的有效性。针对多类问题的扩展也得以实现，其通常采用多个二分类器集成的方案。本研究提出一种基于量子退火的新型量子支持向量机公式，用于直接进行多类分类，称为量子多类支持向量机（QMSVM）。该多类分类问题被构建为可由量子退火求解的单一二次无约束二元优化（QUBO）问题。本研究的主要目标是评估该方法的可行性、精度和时间性能。我们在D-Wave Advantage量子退火器上针对遥感数据分类问题开展了实验。结果表明，尽管量子退火器存在内存需求限制，但QMSVM的精度可与标准支持向量机方法相媲美，且更重要的是，其随训练样本数量的扩展效率显著提高，实现了近乎恒定的时间消耗。本研究展示了一种融合经典计算与量子计算的途径，可利用现有硬件解决遥感领域的实际问题。