论文标题
带有基准HHL溶液的混合量子古典CFD方法论
A Hybrid Quantum-Classical CFD Methodology with Benchmark HHL Solutions
论文作者
论文摘要
量子算法的开发取得了重大进展，用于求解方程的线性系统，并在计算流体动力学（CFD）和类似CFD样问题的情况下应用了越来越多的应用。这项工作通过开发非线性混合量子量子CFD求解器并使用它来生成完全收敛的解决方案来扩展以前的工作。混合求解器使用简单的CFD算法，该算法在许多工业CFD代码中很常见，并将其应用于二维盖子驱动的腔测试案例。这项工作的主题是准备量子电路所需的经典处理时间，重点是将CFD矩阵分解为单位型（LCU）的线性组合。考虑到最大的含有32,767个Pauli琴弦的LCU，CFD网格的最高为65x65节点。提出了一种快速重新计算LCU系数的新方法，尽管这减少了经典的扩展问题而不是消除经典的缩放问题。量子线性方程求解器使用harrow，hassidim，lloyd（HHL）算法通过状态矢量仿真器。从经典的CFD求解器中对测试矩阵进行采样，以研究可以使用HHL实现的溶液准确性。对于最小的5x5和9x9 CFD网格，进行了完整的非线性混合CFD计算。研究了近似LCU和特征值反转电路中的Ancilla旋转数量的影响。初步时序结果表明，混合求解器所需的经典计算机准备时间对于在CFD中获得量子优势同样重要，与量子计算机的时间一样重要。报告的HHL解决方案和LCU分解为将来的研究提供了基准。本研究中使用的CFD测试矩阵可应要求提供。
There has been significant progress in the development of quantum algorithms for solving linear systems of equations with a growing body of applications to Computational Fluid Dynamics (CFD) and CFD-like problems. This work extends previous work by developing a non-linear hybrid quantum-classical CFD solver and using it to generate fully converged solutions. The hybrid solver uses the SIMPLE CFD algorithm, which is common in many industrial CFD codes, and applies it to the 2-dimensional lid driven cavity test case. A theme of this work is the classical processing time needed to prepare the quantum circuit with a focus on the decomposition of the CFD matrix into a linear combination of unitaries (LCU). CFD meshes with up to 65x65 nodes are considered with the largest producing a LCU containing 32,767 Pauli strings. A new method for rapidly re-computing the coefficients in a LCU is proposed, although this reduces, rather than eliminates, the classical scaling issues. The quantum linear equation solver uses the Harrow, Hassidim, Lloyd (HHL) algorithm via a state-vector emulator. Test matrices are sampled from the classical CFD solver to investigate the solution accuracy that can be achieved with HHL. For the smallest 5x5 and 9x9 CFD meshes, full non-linear hybrid CFD calculations are performed. The impacts of approximating the LCU and the varying the number of ancilla rotations in the eigenvalue inversion circuit are studied. Preliminary timing results indicate that the classical computer preparation time needed for a hybrid solver is just as important to the achievement of quantum advantage in CFD as the time on the quantum computer. The reported HHL solutions and LCU decompositions provide a benchmark for future research. The CFD test matrices used in this study are available upon request.
