In our 7th edition of the pCoE QuICC Talks, we will hear Dr. Nana Liu talk about using quantum computer to solve nonlinear partial differential equations.
Title : Quantum computation and the pathways to solve nonlinear partial differential equations
Date/Time : 1-04-2022, 3:00PM IST
Speaker: Dr. Nana Liu
Speaker Bio: Dr. Nana Liu is an Associate Professor at the Shanghai Jiaotong University and also at the Institute of Natural Sciences University of Michigan-Shanghai Jiaotong University Joint Institute. She did her PhD at the University of Oxford and was then a Postdoctoral Fellow at the Centre for Quantum Technologies, NUS in Singapore and at Singapore University of Technology and Design. Her research interests are on the topics of Continuous variable quantum information, quantum machine learning and quantum internet.
Affiliation of the Speaker: University of Michigan-Shanghai Jiaotong University Joint Institute
Abstract: Nonlinear ordinary and partial differential equations have been central to modeling of some of the most significant problems in physics, chemistry, engineering, biology, and finance, including climate modeling, aircraft design, molecular dynamics, and drug design, deep learning neural networks, and financial markets. While quantum computation has shown its advantages for solving linear problems, nonlinear problems have yet remained elusive. This is because quantum mechanics itself is fundamentally linear (as far as we know) and it is not yet known how to model nonlinear problems in a linear way without significant approximations that no longer capture truly nonlinear behavior. Truly nonlinear behavior, however, is what makes real physical systems, like the weather and stock markets, interesting, complex and unpredictable. We show that an important class of nonlinear partial differential equations – Hamilton Jacobi and scalar hyperbolic equations – can indeed be fully captured using a quantum algorithm. These equations are important for many applications like optimal control, machine learning, semi-classical limit of Schrodinger equations, mean-field games and many more. Physical quantities like density and energy (and many more) can be computed using a quantum algorithm that can be up to exponentially more efficient compared to a classical device with respect to the dimension of the system and the error of the final answer. In addition, we provide methods for more general classes of nonlinear partial differential equations and show when speedup with respect to the number of initial conditions can be achieved.