通过谱初始化的量子加速共轭梯度法
Quantum-accelerated conjugate gradient method via spectral initialization
AI总结：
本文提出一种量子加速共轭梯度法，利用容错量子算法生成谱信息初始猜测，以提升求解大规模线性系统效率，展示量子计算在高性能计算中的应用前景。
摘要：
求解大规模线性系统问题是科学和工业计算的核心。经典迭代求解器在未知数数量增大时面临更大困难，而完全量子线性求解器需要容错资源，目前仍无法实现。本文提出一种量子加速共轭梯度（QACG）方法，其中容错量子算法被用于构建一个具有谱信息的初始猜测，供经典共轭梯度（CG）求解器使用。我们估计了集成量子-高性能计算平台求解三维泊松方程的总运行时间和资源需求。QACG的核心特征是可控地将条件数分解到量子和经典求解器之间，从而实现计算努力的灵活分配。在显式的架构假设下，我们识别出QACG在某些情况下比纯经典方法具有更优的运行时间，同时所需的量子资源远少于端到端量子线性求解器。这些结果展示了早期容错量子计算在科学和工业中的应用路径，并指出了一个集成范式，其中量子设备作为高性能计算工作流中的加速器。
英文摘要：
Solving large-scale linear systems problems is a cornerstone in scientific and industrial computing. Classical iterative solvers face increasing difficulty as the number of unknowns becomes large, while fully quantum linear solvers require fault-tolerant resources that remain far beyond near-term feasibility. Here we propose a quantum-accelerated conjugate gradient (QACG) method in which a fault-tolerant quantum algorithm is used exclusively to construct a spectrally informed initial guess for a classical conjugate gradient (CG) solver. We estimate the total runtime and resource requirements of an integrated quantum-HPC platform for the 3D Poisson equation. A central feature of QACG is the controllable decomposition of the condition number between the quantum and the classical solver, enabling flexible allocation of computational effort. Under explicit architectural assumptions, we identify regimes in which QACG yields a runtime advantage over purely classical approaches while requiring substantially fewer quantum resources than end-to-end quantum linear solvers. These results illustrate a concrete pathway toward the scientific and industrial use of early-stage fault-tolerant quantum computing and point to a integrated paradigm in which quantum devices act as accelerators within high-performance computing workflows.
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