用于加速求解稀疏线性系统的优化混合经典-量子算法
Optimised Hybrid Classical-Quantum Algorithm for Accelerated Solution of Sparse Linear Systems
AI总结：
本文提出一种结合CUDA加速预处理与HHL量子算法的混合经典-量子方法，并利用强化学习动态优化参数，以更高效求解大规模稀疏线性系统，在速度、可扩展性及缓解量子算法局限性方面取得提升。
摘要：
高效求解大规模稀疏线性系统在计算科学中构成重大挑战，尤其是在物理、工程、机器学习和金融等领域。随着这些系统规模的增大，传统经典算法面临可扩展性问题，导致性能下降。另一方面，诸如Harrow-Hassidim-Lloyd（HHL）算法等量子算法在求解线性系统方面提供了指数级加速，但它们受到当前量子硬件状态和对矩阵条件数敏感性的制约。本文提出一种混合经典-量子算法，将CUDA加速的预处理技术与HHL算法相结合，以更高效地求解稀疏线性系统。利用经典GPU并行性对矩阵进行预处理和预条件化，降低其条件数，同时采用量子计算通过HHL算法求解预处理后的系统。此外，该算法集成机器学习模型，特别是强化学习，根据实时性能数据动态优化系统参数，如块大小和预处理策略。我们的实验结果表明，所提出的方法不仅在速度和可扩展性上超越了传统方法，而且缓解了量子算法固有的一些局限性。这项工作拓展了高效计算的边界，并为混合计算框架的未来发展奠定了基础。
英文摘要：
Efficiently solving large-scale sparse linear systems poses a significant challenge in computational science, especially in fields such as physics, engineering, machine learning, and finance. Traditional classical algorithms face scalability issues as the size of these systems increases, leading to performance degradation. On the other hand, quantum algorithms, like the Harrow-Hassidim-Lloyd (HHL) algorithm, offer exponential speedups for solving linear systems, yet they are constrained by the current state of quantum hardware and sensitivity to matrix condition numbers. This paper introduces a hybrid classical-quantum algorithm that combines CUDA-accelerated preconditioning techniques with the HHL algorithm to solve sparse linear systems more efficiently. The classical GPU parallelism is utilised to preprocess and precondition the matrix, reducing its condition number, while quantum computing is employed to solve the preconditioned system using the HHL algorithm. Additionally, the algorithm integrates machine learning models, particularly reinforcement learning, to dynamically optimise system parameters, such as block sizes and preconditioning stratgies, based on real-time performance data. Our experimental results show that the proposed approach not only surpasses traditional methods in speed and scalability but also mitigates some of the inherent limitations of quantum algorithms. This work pushes the boundaries of efficient computing and provides a foundation for future advancements in hybrid computational frameworks.
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