[COLLOQUIUM] Quantum Computation of partial differential equations

时   间：  2023-04-14 14:00 — 15:00

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 became challenging for general PDEs, more so for nonlinear ones. Our talk will cover three topics:
1) We introduce the “warped phase transform” to map general linear PDEs and ODEs to Schrodinger equation or with unitary evolution operators in higher dimension so they are suitable for quantum simulation;
2) For (nonlinear) Hamilton-Jacobi equation and scalar nonlinear hyperbolic equations we use the level set method to map them-exactly-to phase space linear PDEs so they can be implemented with quantum algorithms and we gain quantum advantages for various physical and numerical parameters;
3) For PDEs with uncertain coefficients, we introduce a transformation so the uncertainty only appears in the initial data, allowing us to compute ensemble averages with multiple initial data with just one run, instead of multiple runs as in Monte-Carlo or stochastic collocation type sampling algorithms. 

报告人简介：

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，数学科学学院讲席教授，上海国家应用数学中心联合主任，科学工程计算教育部重点实验室主任与人工智能数学基础中心主任。其主要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，机器学习与量子计算等。已在包含Acta Numerica等杂志发表学术论文200余篇。曾获冯康科学计算奖（2001），国际华人数学家大会晨兴数学银奖（2007），入选美国数学会（AMS）首批会士（2012），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），2018年国际数学家大会邀请报告人。