Quantum algorithm for smoothed particle hydrodynamics
Quantum algorithm for smoothed particle hydrodynamics
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DOI：
10.1016/j.cpc.2023.108909
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发表时间：
2020-06
期刊：
影响因子：
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通讯作者：
Rhonda Au-Yeung;A.J.M. Williams;V. Kendon;S. Lind
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文献类型：
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作者：
Rhonda Au-Yeung;A.J.M. Williams;V. Kendon;S. Lind
提出了一种适用于光滑粒子流体动力学（SPH）方法的量子计算算法。我们使用一个规范化的程序编码的SPH算子和域离散化的量子寄存器。然后，我们通过量子寄存器的内积执行SPH求和。使用一维函数，我们测试的方法在经典意义上的内核和一阶和二阶导数的一维函数，使用高斯和Wendland核函数，并比较各种寄存器大小对分析结果。误差收敛在量子比特的数量上是指数快速的。我们扩展的方法来解决一维对流和扩散偏微分方程，这是经常遇到的流体模拟。这项工作为更通用的SPH算法提供了基础，最终导致在基于门的量子计算机上高效模拟复杂的工程问题。
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.