论文标题

使用HHL算法的隐式混合量子古典CFD计算

Implicit Hybrid Quantum-Classical CFD Calculations using the HHL Algorithm

论文作者

Lapworth, Leigh

论文摘要

隐式方法对混合量子式CFD求解器具有吸引力,因为将流程方程组合成单个耦合矩阵,该基质在量子设备上求解,仅在古典设备上留下CFD离散化和基质组件。在本文中,使用模拟HHL电路研究了一个隐式杂交求解器。将混合溶液与包括全本系统分解在内的经典解决方案进行了比较。对HHL特征值反转电路中的量子数的数量如何影响CFD求解器的收敛速率,进行了彻底的分析。在最小和最大特征值中的精度丧失具有不同的影响,并且通过将相应的特征向量与CFD求解器中的误差波联系起来可以理解。鉴定出一种迭代的进料机构,该机制允许在HHL电路中丢失精度以扩大相关的误差波。这些结果将与早期容忍度的CFD应用程序有关,其中每个(逻辑)量子都会计算。良好的经典估计器对最小和最大特征值的重要性也与量子奇异值转换方法的条件数计算矩阵反转的方法有关。

Implicit methods are attractive for hybrid quantum-classical CFD solvers as the flow equations are combined into a single coupled matrix that is solved on the quantum device, leaving only the CFD discretisation and matrix assembly on the classical device. In this paper, an implicit hybrid solver is investigated using emulated HHL circuits. The hybrid solutions are compared with classical solutions including full eigen-system decompositions. A thorough analysis is made of how the number of qubits in the HHL eigenvalue inversion circuit affect the CFD solver's convergence rates. Loss of precision in the minimum and maximum eigenvalues have different effects and are understood by relating the corresponding eigenvectors to error waves in the CFD solver. An iterative feed-forward mechanism is identified that allows loss of precision in the HHL circuit to amplify the associated error waves. These results will be relevant to early fault tolerant CFD applications where every (logical) qubit will count. The importance of good classical estimators for the minimum and maximum eigenvalues is also relevant to the calculation of condition number for Quantum Singular Value Transformation approaches to matrix inversion.

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