报告人：金石（上海交通大学）

时间：2023年12月28日 15:10-

地址：理科楼LA103

摘要：Quantum computers have the potential to gain algebraic and even up to exponential speed up compared with its classical counter parts, 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 will present a systematic way to develop quantum simulation algorithms for general differential equations. Our basic framework is dimension lifting, that transfers nonlinear PDEs to linear ones, and linear ones to Schrodinger type of PDEs. For non-autonomous PDEs and ODEs, or Hamiltonian systems with time-dependent Hamiltonians, we also add an extra dimension to transform them into autonomous PDEs that have only time-independent coefficients, thus quantum simulations can be done without using the cumbersome Dyson's series and time-ordering operators. Our formulation allows both qubit and qumode (continuous-variable) formulations, and their hybridizations.

简介：金石，欧洲人文和自然科学院外籍院士，欧洲科学院院士，上海交通大学自然科学研究院院长，上海交通大学数学科学学院讲席教授，上海国家应用数学中心联席主任，上海交通大学重庆人工智能研究院院长。本科毕业于北京大学数学系，博士毕业于美国亚利桑那大学，历任美国纽约大学库朗数学研究所博士后，美国佐治亚理工学院助理教授、副教授，美国威斯康星大学（麦迪逊）正教授，数学系系主任，Vilas 杰出成就教授。他曾获冯康科学计算奖（2001），国家自然科学基金杰出青年基金（2002）、国际华人数学家大会晨兴数学奖（2007）。他是美国数学会（AMS）首批会士（2012），国际工业与应用数学学会(SIAM)会士（2013），中国工业与应用数学学会（CSIAM）首批会士（2020），及2018年国际数学大会（ICM）邀请报告人。2021年他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。他的研究方向包括双曲型守恒律方程，量子动力学，不确定性量化，交互粒子系统，计算流体力学，机器学习与量子计算等。他在包含Acta Numerica等杂志发表过190余篇学术论文。

邀请人：穆春来    邱越

欢迎广大师生积极参与！