论文标题
通过经典集成方法求解普通微分方程的量子算法
Quantum Algorithms for Solving Ordinary Differential Equations via Classical Integration Methods
论文作者
论文摘要
识别适合（未来）量子计算机的计算任务是一个积极的研究领域。在这里，我们探索利用量子计算机以求解微分方程的目的。我们考虑了两种方法：（i）在数字量子计算机上对基础编码和定点算术进行编码，（ii）代表和求解高阶runge-kutta方法是量子退火器上的优化问题。当实现应用于二维线性普通微分方程时，我们设计和模拟了相应的数字量子电路，并在D-Wave 2000Q上实现并运行6 $^{\ MATHRM {TH} $ order Gauss-Legendre搭配方法，与参考解决方案显示良好的一致性。我们发现，量子退火方法具有高阶隐式整合方法的最大潜力。作为有希望的未来情况，数字算术方法可以用作量子搜索算法中的“甲骨文”。
Identifying computational tasks suitable for (future) quantum computers is an active field of research. Here we explore utilizing quantum computers for the purpose of solving differential equations. We consider two approaches: (i) basis encoding and fixed-point arithmetic on a digital quantum computer, and (ii) representing and solving high-order Runge-Kutta methods as optimization problems on quantum annealers. As realizations applied to two-dimensional linear ordinary differential equations, we devise and simulate corresponding digital quantum circuits, and implement and run a 6$^{\mathrm{th}}$ order Gauss-Legendre collocation method on a D-Wave 2000Q system, showing good agreement with the reference solution. We find that the quantum annealing approach exhibits the largest potential for high-order implicit integration methods. As promising future scenario, the digital arithmetic method could be employed as an "oracle" within quantum search algorithms for inverse problems.
