基于QUBO的SVM训练中权重离散化的影响
On the Impact of Weight Discretization in QUBO-Based SVM Training
摘要：
训练支持向量机（SVM）可以被公式化为一个QUBO问题，使得能够使用量子退火进行模型优化。在这项工作中，我们研究了量子位的数量-与双权重的离散化水平相关-如何影响数据集的预测性能。我们将基于QUBO的SVM训练与经典的LIBSVM求解器进行了比较，发现即使是低精度的QUBO编码（例如，每个参数1位）产生有竞争力的，有时是优越的精度。虽然增加的位深度可以实现更大的正则化参数，但它并不总是改善分类。我们的研究结果表明，选择正确的支持向量可能比精确的权重更重要。虽然目前的硬件限制了可解QUBO的大小，但我们的研究结果突出了量子退火在量子设备规模化时用于有效SVM训练的潜力。
英文摘要：
Training Support Vector Machines (SVMs) can be formulated as a QUBO problem, enabling the use of quantum annealing for model optimization. In this work, we study how the number of qubits - linked to the discretization level of dual weights - affects predictive performance across datasets. We compare QUBO-based SVM training to the classical LIBSVM solver and find that even low-precision QUBO encodings (e.g., 1 bit per parameter) yield competitive, and sometimes superior, accuracy. While increased bit-depth enables larger regularization parameters, it does not always improve classification. Our findings suggest that selecting the right support vectors may matter more than their precise weighting. Although current hardware limits the size of solvable QUBOs, our results highlight the potential of quantum annealing for efficient SVM training as quantum devices scale.
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