Exact Quantum Model Reduction for Lindblad Dynamics

Obtaining simpler models that can accurately reproduce relevant features of a complex quantum-dynamical system of interest is crucial for improving the efficiency of simulation on either classical or quantum computers. We focus on finite-dimensional many-body Markovian quantum systems described by a Lindblad master equation, and show how a systematic model-reduction approach based on Krylov operator subspaces may be obtained by leveraging information on initial conditions and observables of interests. The obtained models are provably the smallest linear models that exactly reproduce the target evolution. Notably, by extending these operator subspaces to operator algebras, reduced models that preserve the complete-positivity constraint of physically admissible quantum dynamics may be constructed, as required for implementation on a quantum simulator. Illustrative applications to open many-body systems of relevance to condensed-matter and quantum-information physics are discussed, along with possible extensions to controlled Lindblad generators.