Model Reduction for Controlled Quantum Markov Dynamics

TL;DR

This paper develops a method for reducing the complexity of controlled quantum Markov systems, ensuring accurate observable evolution and maintaining the physical Lindblad structure, using Krylov subspaces and operator algebra techniques.

Contribution

It introduces a novel model reduction technique for time-dependent Lindblad quantum systems that preserves the dynamics of key observables and the Lindblad form.

Findings

Exact reproduction of observable evolution in reduced models

Guarantees the reduced model remains in Lindblad form

Applicable to systems with external control

Abstract

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.