This paper investigates the application of Quantum Support Vector Machines (QSVMs) with an emphasis on the computational advancements enabled by NVIDIA's cuQuantum SDK, especially leveraging the cuTensorNet library. We present a simulation workflow that substantially diminishes computational overhead, as evidenced by our experiments, from exponential to quadratic cost. While state vector simulations become infeasible for qubit counts over 50, our evaluation demonstrates that cuTensorNet speeds up simulations to be completed within seconds on the NVIDIA A100 GPU, even for qubit counts approaching 784. By employing multi-GPU processing with Message Passing Interface (MPI), we document a marked decrease in computation times, effectively demonstrating the strong linear speedup of our approach for increasing data sizes. This enables QSVMs to operate efficiently on High-Performance Computing (HPC) systems, thereby opening a new window for researchers to explore complex quantum algorithms that have not yet been investigated. In accuracy assessments, our QSVM achieves up to 95\% on challenging classifications within the MNIST dataset for training sets larger than 100 instances, surpassing the capabilities of classical SVMs. These advancements position cuTensorNet within the cuQuantum SDK as a pivotal tool for scaling quantum machine learning simulations and potentially signpost the seamless integration of such computational strategies as pivotal within the Quantum-HPC ecosystem.

翻译：本文聚焦于量子支持向量机（QSVM）的应用研究，重点探讨了NVIDIA cuQuantum SDK（特别是cuTensorNet库）所驱动的计算性能提升。我们提出了一种模拟工作流，可将计算开销从指数级显著降低至二次级——实验证实了该方法的有效性。当量子比特数超过50时，态矢量模拟已不可行，但我们的评估表明，即使在量子比特数接近784的情况下，cuTensorNet也能在NVIDIA A100 GPU上实现秒级模拟加速。通过采用基于消息传递接口（MPI）的多GPU处理，我们观察到计算时间显著缩减，充分展示了该方法随数据规模增长呈现的强线性加速特性。这使得QSVM能够在高性能计算（HPC）系统上高效运行，为研究者探索尚未涉足的复杂量子算法开辟了新窗口。在精度评估中，针对MNIST数据集超过100个训练样本的复杂分类任务，我们的QSVM准确率高达95%，超越了经典支持向量机。这些进展将cuQuantum SDK中的cuTensorNet确立为扩展量子机器学习模拟规模的关键工具，同时也预示着此类计算策略将无缝集成到量子-HPC生态系统中。