12 May 2024 | Junpeng Hu, Shi Jin, Nana Liu, Lei Zhang
This paper presents a detailed implementation of a quantum algorithm for solving general partial differential equations (PDEs) using Schrödingerisation techniques. Schrödingerisation involves transforming general linear PDEs into Schrödinger-type equations, allowing the application of quantum algorithms designed for these equations. The authors provide explicit quantum circuit implementations for the heat equation and the advection equation, demonstrating the effectiveness of their approach through numerical experiments. Complexity analysis is performed to show that the quantum algorithms offer significant advantages over classical methods in high dimensions. The paper also includes a detailed discussion on the scalability and efficiency of the quantum circuits, highlighting the potential for quantum advantage in solving complex PDEs.This paper presents a detailed implementation of a quantum algorithm for solving general partial differential equations (PDEs) using Schrödingerisation techniques. Schrödingerisation involves transforming general linear PDEs into Schrödinger-type equations, allowing the application of quantum algorithms designed for these equations. The authors provide explicit quantum circuit implementations for the heat equation and the advection equation, demonstrating the effectiveness of their approach through numerical experiments. Complexity analysis is performed to show that the quantum algorithms offer significant advantages over classical methods in high dimensions. The paper also includes a detailed discussion on the scalability and efficiency of the quantum circuits, highlighting the potential for quantum advantage in solving complex PDEs.