报告题目：Quantum computation of partial differential equations

报告摘要：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 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 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, and provides the foundation for analog quantum computing.

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，美国数学学会首批会士，美国工业与应用数学学会会士，中国工业与应用数学学会会士，教育部第四批长江学者讲座教授。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，国际华人数学家大会晨兴数学银奖、国家杰出青年科学基金（杰青B类）等多项荣誉，为2018年国际数学家大会邀请报告人。担任Commun. Math. Sci.的创刊及现任主编，并担任过十多个国际著名计算和应用数学杂志的编委。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。

报告时间：2024年05月23日 10:15—11:15

报告地点：同析4号楼 322会议室