【报告人】金石教授

【报告题目】Quantum algorithms for nonlinear partial differential equations

【报告摘要】

（1）Nonlinear partial differential equations (PDEs) are crucial to modelling important problems in science but they are computationally expensive and suffer from the curse of dimensionality. Since quantum algorithms have the potential to resolve the curse of dimensionality in certain instances, some quantum algorithms for nonlinear PDEs have been developed. However, they are fundamentally bound either to weak nonlinearities, valid to only short times, or display no quantum advantage. We construct new quantum algorithms--based on level sets --for nonlinear Hamilton-Jacobi and scalar hyperbolic PDEs that can be performed with quantum advantages on various critical numerical parameters, even for computing the physical observables, for arbitrary nonlinearity and are valid globally in time.

（2）PDEs are important for many applications like optimal control, machine learning, semi-classical limit of Schrodinger equations, mean-field games and many more. Depending on the details of the initial data, it can display up to exponential advantage in both the dimension of the PDE and the error in computing its observables.  For general nonlinear PDEs, quantum advantage with respect to M, for computing the ensemble averages of solutions corresponding to M different initial data, is possible in the large $M$ limit.

【报告时间】2022年6月4日，上午14：00——17:00

【报告形式】腾讯会议；会议号：214 905 299

【报告人简介】金石，上海交通大学自然科学研究院院长，数学学院讲席教授。2021年当选为欧洲人文和自然科学院外籍院士。先后获北京大学学士学位，美国亚利桑那大学博士学位，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，上海交通大学数学系讲席教授、系主任。同时担任上海应用数学中心联合主任，上海交通大学教育部科学工程计算重点实验室主任与人工智能数学基础中心主任。是冯康科学计算奖获得者，美国数学会首批会士，工业与应用数学学会会士，及2018年国际数学家大会邀请报告人。研究方向包括动理学理论，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，计算流体力学等。在包含Acta Numerica等杂志发表过170余篇学术论文，论文获得过Springer杂志Research in the Mathematical Sciences创刊5年来四篇最佳论文奖之一，及入选World Scientific 杂志2019年最佳论文。