题目：New progress in quantum computation of partial differential equations and related problems
报告人： 金石，上海交通大学
报告时间： 10月30日10:00
报告地点： 卓越楼810
报告摘要：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. It is important to explore whether other problems in scientific computing, such as ODEs, PDEs, and linear algebra that arise in both classical and quantum systems which are not unitary evolution, can be handled by quantum computers.
We will present a systematic way to develop quantum simulation algorithms for general differential equations. Our basic framework is dimension lifting, that transfers non-autonomous ODEs/PDEs systems to autonomous ones, nonlinear PDEs to linear ones, and linear ones to Schrodinger type PDEs—coined “Schrodingerization”—with uniform evolutions. Our formulation allows both qubit and qumode (continuous-variable) formulations, and their hybridizations, and provides the foundation for analog quantum computing which are easier to realize in the near term. We will present dimension lifting techniques for quantum simulation of stochastic DEs and PDEs with fractional derivatives, and quantum machine learning. A quantum simulation software—“Unitary Lab”—will also be introduced.
报告人简介：金石，上海交通大学数学科学学院讲席教授，欧洲人文和自然科学院外籍院士，欧洲科学院院士，国际数学家大会邀请报告人，国家杰出青年科学基金获得者，美国数学学会会士，SIAM会士，CSIAM会士，教育部长江学者讲座教授。现任上海交通大学自然科学研究院院长，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。曾获冯康科学计算奖、上海市自然科学一等奖等多项奖项。主要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。