Prof. Shi Jin

Foreign Member of Academia European, Inaugural Fellow of the American Mathematical Society, Shanghai Jiao Tong University, China 

Title：Schrodingerization of ordinary and partial differential equation in quantum computing 

Abstract

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, a linear PDE evolved by unitary operators.  The most efficient quantum PDE solver is quantum simulation based on solving the Schrodinger equation. The evolution operators of other differential equations are in general not  unitary  thus cannot be directly solved by quantum computation. 

We introduce a generic technology, called “Schrodingertization”, that transforms any linear ODEs and PDEs into Schrodinger-type PDEs in one higher dimension in the Fourier space. The method also works for boundary value and interface problems and linear algebra iterative solvers, allowing all this problem suitable for quantum simulation. For (nonlinear) Hamilton-Jacobi equation and scalar nonlinear hyperbolic equations we use the level set method to map them—exactly—to phase space linear PDEs so they can be implemented with quantum algorithms and we gain quantum advantages for various physical and numerical parameters.  Another advantage of our formulation is that it is suitable for both qubit formalism and continuous-variable (qumodes) formalism, the latter convenient for more near-term analogy quantum computation. 

Biography

Prof. Shi Jin is the Director of Institute of Natural Sciences, and Chair Professor of Mathematics, at Shanghai Jiao Tong University. He is also a co-director of the Shanghai Center of Applied Mathematics. He obtained his BS degree from Peking University and his Ph.D. from University of Arizona. He was a postdoc at Courant Institute, New York University, an assistant and associate professors at Georgia Institute of Technology, and a full professor, department chair and Vilas Distinguished Achievement Professor at University of WisconsinMadison, Chair of Department of Mathematics at Shanghai Jiao Tong University. He received a Feng Kang Prize of Scientific Computing in 2001 and a Morningside Silver Medal of Mathematics at the International Congress of Chinese Mathematicians in 2007. He is an inaugural Fellow of the American Mathematical Society (AMS) (2012), a Fellow of Society of Industrial and Applied Mathematics (SIAM) (2013), an inaugural Fellow of the China Society for Industrial and Applied Mathematics (CSIAM) (2020), and an Invited Speaker at the International Congress of Mathematicians in 2018.