Learning the dynamics of open quantum systems from local measurements

The increasing complexity of engineered quantum systems and devices raises the need for efficient methods to verify that these systems are indeed performing the desired quantum dynamics. Due to the inevitable coupling to external environments, these methods should obtain not only the unitary part of the dynamics, but also the dissipation and decoherence affecting the system's dynamics. Here, we propose a method for reconstructing the Lindbladian governing the Markovian dynamics of open many-body quantum systems, using data obtained from local measurements on their steady states. We show that the number of measurements and computational resources required by the method are polynomial in the system size. For systems with finite-range interactions, the method recovers the Linbladian acting on each finite spatial domain using only observables within that domain. We numerically study the accuracy of the reconstruction as a function of the number of measurements, type of open-system dynamics and system size. Interestingly, we show that couplings to external environments can in fact facilitate the reconstruction of Hamiltonians composed of commuting terms.