Researchers have developed an algorithm for learning local Lindbladians, which describe the evolution of open quantum systems, by accessing their dynamics. The goal is to estimate both the Hamiltonian and dissipative coefficients that characterize these systems. The proposed method is near-optimal in terms of its use of dynamical evolution and total evolution time, representing a significant advance in the characterization of complex quantum systems.

The algorithm relies on finite-time channel probes, where the unknown evolution is run for short periods. From these evolutions, Pauli transfer matrices are estimated using classical shadows. Subsequently, these estimates are converted into Lindbladian coefficients via stable local Fourier inversions. This approach is non-adaptive, requires no ancillas, and uses only random product states as inputs, followed by random Pauli measurements. Furthermore, it does not require prior knowledge of the Lindbladian's support.

For fixed locality and bounded dissipative site degree, the use of dynamical evolution and total evolution time scale as $\widetilde{O}(\Lambda^2/\varepsilon^2)$ and $\widetilde{O}(\Lambda/\varepsilon^2)$ respectively, where $\Lambda$ is the local dynamical strength bound and $\varepsilon$ is the target accuracy, with only logarithmic dependence on the number of qubits. The researchers complement the algorithm with matching lower bounds, demonstrating that the learning algorithm is near-optimal. Notably, the lower bounds imply that the Heisenberg-limited scaling achievable for Hamiltonian learning is information-theoretically impossible when dissipative coefficients must also be estimated.