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荔园学者Colloquium第八十九期

讲座题目: Dimension lifting for quantum computation of partial differential equations

主讲人：金石 教授 （上海交通大学）

讲座时间：2024年7月30日下午15：00-16：00

讲座地点：深圳大学粤海校区汇星楼514

内容摘要：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.

主讲人简介：金石，现为上海交通大学自然科学研究院院长，数学学院讲席教授。他同时担任上海国家应用数学中心联合主任与上海交通大学重庆人工智能研究院院长。他是美国数学会首批会士， 美国工业与应用数学学会会士， 和2018年国际数学家大会邀请报告人， 并于2021年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。

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2024年7月27日