Boundary Treatment for Variational Quantum Simulations of Partial Differential Equations on Quantum Computers

The data refers to a variational quantum algorithm experiments solving initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum computers of the current noisy intermediate-scale quantum era. The partial differential equation is initially translated into an optimal control problem with a modular control-to-state operator (ansatz). The examples include steady and unsteady diffusive transport equations for a scalar property in combination with various Dirichlet, Neumann, or Robin conditions. The results are complemented by classical finite difference results, which have been taken for comparison in the underlying document (arXiv.2402.18619).

本数据集对应用于求解二阶偏微分方程描述的初边值问题的变分量子算法（variational quantum algorithm）实验。该方案采用经典-量子混合硬件架构，适配当前含噪中等规模量子（noisy intermediate-scale quantum, NISQ）时代的量子计算机。研究首先将偏微分方程转化为带有模块化控制-状态算子试探方案（ansatz）的最优控制问题。测试示例涵盖标量属性的稳态与非稳态扩散输运方程，并搭配多种狄利克雷（Dirichlet）、诺依曼（Neumann）或罗宾（Robin）边界条件。本研究结果辅以经典有限差分方法的计算结果，相关对比数据已在预印本文档arXiv.2402.18619中给出。