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：本文着重研究了量子支持向量机（QSVM）的应用，并重点探讨了NVIDIA cuQuantum SDK（特别是利用cuTensorNet库）所实现的算力突破。我们提出了一种模拟工作流，该工作流显著降低了计算开销——实验证明，其成本从指数级降至二次级。尽管状态向量模拟在量子比特数超过50时变得不可行，但我们的评估表明，即使量子比特数接近784，cuTensorNet仍能在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，我们记录到计算时间显著缩短，有效展示了该方法随数据量增大而呈现的强线性加速比。这使得QSVM能够在高性能计算（HPC）系统上高效运行，从而为研究人员探索尚未被研究的复杂量子算法打开了新窗口。在精度评估中，当训练集规模超过100个样本时，我们的QSVM在MNIST数据集的挑战性分类任务上达到了95%的准确率，超越了经典SVM的能力。这些进展将cuQuantum SDK中的cuTensorNet定位为扩展量子机器学习模拟规模的关键工具，并很可能预示着此类计算策略作为量子-HPC生态系统的核心组成部分实现无缝集成。