報告題目：Dimension Lifting for Quantum Computation of partial differential equations and related problems
報 告 人：金石 教授 上海交通大學
報告時間：2024年3月27日 15:00
報告地點：正新樓209
校内聯系人：張然 zhangran@jlu.edu.cn
報告摘要：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.
報告人簡介： 金石，現為上海交通大學自然科學研究院院長，伟德线上平台講席教授。他同時擔任上海國家應用數學中心聯合主任與上海交通大學重慶人工智能研究院院長。他是美國數學會首批會士， 美國工業與應用數學學會會士， 和2018年國際數學家大會邀請報告人， 并于2021年當選為歐洲人文與自然科學院(Academia Europaea)外籍院士與歐洲科學院(European Academy of Sciences)院士。他的研究方向包括科學計算，動理學理論，多尺度計算，計算流體力學, 不确定性量化，機器學習與量子計算等。
