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Quantum simulation of discrete linear dynamical systems and simple iterative methods in linear algebra via Schrodingerisation
Shi Jin, Nana Liu
Quantum simulation is known to be capable of simulating certain dynamical systems in continuous time -- Schrodinger's equations being the most direct and well-known -- more efficie…
Quantum algorithms for uncertainty quantification: application to partial differential equations
Francois Golse, Shi Jin, Nana Liu
Most problems in uncertainty quantification, despite its ubiquitousness in scientific computing, applied mathematics and data science, remain formidable on a classical computer. Fo…
Time complexity analysis of quantum algorithms via linear representations for nonlinear ordinary and partial differential equations
Shi Jin, Nana Liu, Yue Yu
We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations (HJE…
Quantum algorithms for computing observables of nonlinear partial differential equations
Shi Jin, Nana Liu
We construct quantum algorithms to compute physical observables of nonlinear PDEs with M initial data. Based on an exact mapping between nonlinear and linear PDEs using the level s…