论文标题
变化量子演化方程求解器
Variational Quantum Evolution Equation Solver
论文作者
论文摘要
变性量子算法为近期量子计算机上的部分微分方程提供了有希望的新范式。在这里，我们提出了一种通过隐式时间步长的拉普拉斯运算符来求解通用演化方程的变分量子算法。与随机重新定位相比，通过溶液矢量先前的媒介媒介告知编码的源状态会导致收敛速度更快。通过对热方程的状态向量仿真，我们演示了算法的时间复杂性如何用ANSATZ体积进行梯度估计以及如何使用扩散参数尺度。我们提出的算法在经济上扩展到高阶时间稳定方案，例如曲柄 - 尼科尔森方法。我们提出了一种半图案方案，用于求解具有非线性术语的进化方程系统，例如反应扩散和不可压缩的Navier-Stokes方程，并通过概念概念的结果证明其有效性。
Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. Here, we propose a variational quantum algorithm for solving a general evolution equation through implicit time-stepping of the Laplacian operator. The use of encoded source states informed by preceding solution vectors results in faster convergence compared to random re-initialization. Through statevector simulations of the heat equation, we demonstrate how the time complexity of our algorithm scales with the ansatz volume for gradient estimation and how the time-to-solution scales with the diffusion parameter. Our proposed algorithm extends economically to higher-order time-stepping schemes, such as the Crank-Nicolson method. We present a semi-implicit scheme for solving systems of evolution equations with non-linear terms, such as the reaction-diffusion and the incompressible Navier-Stokes equations, and demonstrate its validity by proof-of-concept results.
