Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for its classically challenging representational capacity, notable improvements in average precision compared to classical counterparts were observed in previous studies. Conventional calculations of these kernels, however, present a quadratic time complexity concerning data size, posing challenges in practical applications. To mitigate this, we explore two distinct approaches: utilizing randomized measurements to evaluate the quantum kernel and implementing the variable subsampling ensemble method, both targeting linear time complexity. Experimental results demonstrate a substantial reduction in training and inference times by up to 95\% and 25\% respectively, employing these methods. Although unstable, the average precision of randomized measurements discernibly surpasses that of the classical Radial Basis Function kernel, suggesting a promising direction for further research in scalable, efficient quantum computing applications in machine learning.

翻译：量子计算凭借其增强各类机器学习任务的潜力，推动了核计算与模型精度的显著进步。结合一类支持向量机与量子核（该核具有经典计算难以实现的表征能力），前人研究发现相比经典对照方法，平均精度得到明显改善。然而，这些核的传统计算在数据规模上呈现二次时间复杂性，为实际应用带来挑战。为缓解此问题，我们探索两种不同方法：利用随机测量评估量子核，以及采用可变子采样集成方法，两者均以线性时间复杂性为目标。实验结果表明，采用这些方法后，训练与推理时间分别显著缩短达95%和25%。尽管随机测量的平均精度存在不稳定性，但其已明显超越经典径向基函数核的精度，这为机器学习中可扩展、高效的量子计算应用研究指出了富有前景的方向。