Dimension Lifting for Quantum Computation of partial differential equations and related problems
报告专家：金石（上海交通大学自然科学研究院）
报告时间：2024年10月18日（星期五）, 10:00-11:00
报告地点：西南数学中心516报告厅
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.
专家简介：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，上海交通大学数学科学学院讲席教授。他的研究领域包括动理学理论、双曲型守恒律方程、计算流体力学、量子动力学、不确定性量化、交互粒子系统和分子动力学及机器学习等，在双曲型方程的松弛格式、多尺度动理学方程的渐近保持格式、量子动力学的半经典计算方法及交互粒子系统随机分批方法等方面的研究工作具有广泛影响，主要工作发表在Acta Numerica和Comm. Pure Appl. Math.等顶尖杂志，曾应邀在国际数学家大会作45分钟报告。
邀请人：王宝富
