论文标题
平滑颗粒流体动力学的量子算法
Quantum Algorithm for Smoothed Particle Hydrodynamics
论文作者
论文摘要
我们提出了平滑粒子流体动力学（SPH）方法的量子计算算法。我们使用归一化过程来编码量子寄存器中的SPH运算符和域离散化。然后，我们通过量子寄存器的内部产物执行SPH求和。使用一维函数，我们使用Gaussian和Wendland内核函数以经典的含义和一维函数的第一和第二个衍生物来测试该方法，并将各种寄存器大小与分析结果进行比较。错误收敛在量子数的数量中呈指数级快速。我们扩展了解决一维对流和扩散部分微分方程的方法，这些方程通常在流体模拟中遇到。这项工作为更通用的SPH算法奠定了基础，最终导致了对基于门的量子计算机上复杂工程问题的高效模拟。
We present a quantum computing algorithm for the smoothed particle hydrodynamics (SPH) method. We use a normalization procedure to encode the SPH operators and domain discretization in a quantum register. We then perform the SPH summation via an inner product of quantum registers. Using a one-dimensional function, we test the approach in a classical sense for the kernel sum and first and second derivatives of a one-dimensional function, using both the Gaussian and Wendland kernel functions, and compare various register sizes against analytical results. Error convergence is exponentially fast in the number of qubits. We extend the method to solve the one-dimensional advection and diffusion partial differential equations, which are commonly encountered in fluids simulations. This work provides a foundation for a more general SPH algorithm, eventually leading to highly efficient simulations of complex engineering problems on gate-based quantum computers.
