论文标题
用于流体动力学应用的对流扩散方程的变异量子解决方案
Variational Quantum Solutions to the Advection-Diffusion Equation for Applications in Fluid Dynamics
论文作者
论文摘要
功耗和计算功率的限制限制了通过经典计算方法的操作数值天气预测的技能。量子计算可能有可能解决这两个挑战。本文中，我们提出了一种使用量子计算的流体动力学计算方法。这种结合多种算法的混合量子古典方法对数与矢量空间的尺寸缩放，并在单一操作员的线性组合中与非零项的数量进行四次缩放，以指定线性运算符的线性操作员描述了感兴趣的系统。作为演示，我们使用我们的方法来解决使用IBM量子计算机的小型系统的对流扩散方程。我们发现，即使是当今可用的嘈杂量子计算机，也可以在方程式的可靠解决方案中获得。利用量子计算机的这种方法和其他方法可以在数值天气预测中取代我们的一些传统方法，因为量子硬件继续改善。
Constraints in power consumption and computational power limit the skill of operational numerical weather prediction by classical computing methods. Quantum computing could potentially address both of these challenges. Herein, we present one method to perform fluid dynamics calculations that takes advantage of quantum computing. This hybrid quantum-classical method, which combines several algorithms, scales logarithmically with the dimension of the vector space and quadratically with the number of nonzero terms in the linear combination of unitary operators that specifies the linear operator describing the system of interest. As a demonstration, we apply our method to solve the advection-diffusion equation for a small system using IBM quantum computers. We find that reliable solutions of the equation can be obtained on even the noisy quantum computers available today. This and other methods that exploit quantum computers could replace some of our traditional methods in numerical weather prediction as quantum hardware continues to improve.
