论文标题
通过Schrodingeration对部分微分方程进行量子模拟：技术细节
Quantum simulation of partial differential equations via Schrodingerisation: technical details
论文作者
论文摘要
我们研究了一种新方法 - 称为[Jin，liu，Yu，arxiv：2212.13969]中引入的schrodingeratization-用于用量子模拟求解通用线性偏微分方程。该方法使用称为扭曲的相变的新的简单转换，将线性部分微分方程转换为“ schRostrized”或Hamiltonian系统。在这里，我们提供了更深入的技术讨论，并以更详细和教学的方式扩展这种方法。我们将其应用于更多偏微分方程的示例，包括热，对流，Fokker-Planck，Linear Boltzmann和Black-Scholes方程。该方法还可以扩展到schrodinger的一般线性偏微分方程，包括vlasov-fokker-planck方程和非线性普通微分方程的liouville表示方程。
We study a new method - called Schrodingerisation introduced in [Jin, Liu, Yu, arXiv: 2212.13969] - for solving general linear partial differential equations with quantum simulation. This method converts linear partial differential equations into a `Schrodingerised' or Hamiltonian system, using a new and simple transformation called the warped phase transformation. Here we provide more in-depth technical discussions and expand on this approach in a more detailed and pedagogical way. We apply this to more examples of partial differential equations, including heat, convection, Fokker-Planck, linear Boltzmann and Black-Scholes equations. This approach can also be extended to Schrodingerise general linear partial differential equations, including the Vlasov-Fokker-Planck equation and the Liouville representation equation for nonlinear ordinary differential equations.
