Quantum simulation of discrete linear dynamical systems and simple iterative methods in linear algebra via Schrodingerisation

Understand

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 efficiently than classical simulation.

• Any linear dynamical system can in fact be transformed into a system of Schrodinger's equations via a method called Schrodingerisation.
• Building on the observation that iterative methods in linear algebra, and more generally discrete linear dynamical systems, can be viewed as discrete time approximations of dynamical systems which evolve continuously in time, we can apply the Schrodingerisation technique.
• Thus quantum simulation can be directly applied to the continuous-time limits of some of the simplest iterative methods.