讲座题目：基于“薛定谔化”的偏微分方程的量子算法
主讲人：金石 院士
开始时间：2025-03-16 08:00
讲座地址：闵行校区数学楼102报告厅
主办单位：数学科学学院
报告人简介：
金石，现为上海交通大学自然科学研究院院长，数学学院讲席教授。他同时担任上海国家应用数学中心联合主任与上海交通大学重庆人工智能研究院院长。他是美国数学会首批会士(2012)， 美国工业与应用数学学会会士(2013)， 和2018年国际数学家大会邀请报告人，并于2021年当选为欧洲人文与自然科学院(Academia Europaea)外籍院士与欧洲科学院(European Academy of Sciences)院士。2024年他获得上海市自然科学一等奖。他的研究方向包括科学计算，动理学理论，多尺度计算，计算流体力学, 不确定性量化，机器学习与量子计算等。
报告内容简介：
Quantum computers have the potential to gain algebraic and even up to exponential speed up compared with its classical counterparts, and can lead to technology revolution in the 21st century. Since quantum computers are designed based on quantum mechanics principle, they are most suitable to solve the Schrodinger equation, and linear PDEs (and ODEs) evolved by unitary operators. The most efficient quantum PDE solver is quantum simulation based on solving the Schrodinger equation. It will be interesting to explore what other problems in scientific computing, such as ODEs, PDEs, and linear algebra that arise in both classical and quantum systems, can be handled by quantum simulation. We provide a novel and generic method, called "Schrodingerization", that maps, in one-higher dimension, any linear ODEs and PDEs to Schrodinger type PDEs with unitary evolution. This allows quantum simulation for general linear PDEs and ODEs, in both continuous varialble (qumodes) and qubits based frameworks, the former suitable for analog quantum computing. We will also present other dimension lifting techniques that transfer nonlinear PDEs to linear ones, and and non-autonomous PDEs and ODEs with time-dependent coefficients to autonomous ones.
