Vortrag
Efficient quantum computation for partial differential equations
Vortrag von Prof. Dr. Nana Liu
Datum: 06.03.23 Zeit: 13.15 - 14.15 Raum: ETH HG G 19.2
What kinds of scientific computing problems are suited to be solved on a quantum device with quantum advantage? It turns out that by transforming a partial differential equation (PDE) into a higher-dimensional space, certain important issues can be resolved while at the same time not incurring a curse of dimensionality, when performed with a quantum algorithm. In this talk, I’ll explore ways in which quantum algorithms can be used to efficiently solve not just linear PDEs but also certain classes of nonlinear PDEs, like nonlinear Hamilton-Jacobi equations and scalar hyperbolic equations, based on the level-set formalism. Using another transformation, PDEs with uncertainty can be tackled. I’ll also introduce a simple new way–called Schrodingerisation– to simulate general linear partial differential equations via quantum simulation. Using a simple new transform and introducing one extra dimension, any linear partial differential equation can be recast into a system of Schrodinger’s equations – in real time — in a straightforward way. This approach is not only applicable to PDEs for classical problems but also those for quantum problems – like the preparation of quantum ground states, Gibbs states and the simulation of quantum states in random media in the semiclassical limit. In this talk, I’ll explore ways in which quantum algorithms can be used to efficiently solve not just linear PDEs but also certain classes of nonlinear PDEs, like nonlinear Hamilton-Jacobi equations and scalar hyperbolic equations, based on the level-set formalism. Using another transformation, PDEs with uncertainty can be tackled. I’ll also introduce a simple new way–called Schrodingerisation– to simulate general linear partial differential equations via quantum simulation. Using a simple new transform and introducing one extra dimension, any linear partial differential equation can be recast into a system of Schrodinger’s equations – in real time — in a straightforward way. This approach is not only applicable to PDEs for classical problems but also those for quantum problems – like the preparation of quantum ground states, Gibbs states and the simulation of quantum states in random media in the semiclassical limit.