Model Reduction for Controlled Quantum Markov Dynamics

We consider the problem of model reduction for Markovian quantum systems whose dynamics are described by a time-dependent Lindblad generator – notably, as arising in the presence of external control. Our approach, which builds upon Krylov operator subspaces and operator-algebraic techniques introduced for time-independent generators, returns a reduced model that reproduces exactly the evolution of observables of interest and is guaranteed to be in Lindblad form.