Learning the structure of open quantum systems

We design an algorithm for learning the coefficients of a local Lindbladian given access to its real-time evolution. Though Lindbladians present new challenges not present in the special case of Hamiltonians, our algorithm achieves the suite of desiderata attained by state-of-the-art Hamiltonian learning algorithms: (1) it uses non-adaptive, ancilla-free randomized Pauli measurement circuits with a constant time resolution (2) it works without knowledge of the structure of the unknown Lindbladian; (3) it works for long-range Lindbladians. Moreover, we prove a lower bound showing that our algorithm is optimal in each parameter up to logarithmic factors.

Our algorithm is a simple iterative method, and its analysis identifies the difficulty unique to open systems, which we call “confusing” terms. For settings where the “confusion” is limited, the performance of the algorithm improves. We demonstrate this for the case of structure learning of Hamiltonians from access to real-time evolution, where we obtain a new, control-free algorithm that is significantly simpler than previous work. In addition, using the same iterative method, we design the first efficient algorithm for structure learning Hamiltonians from high-temperature Gibbs states.

Based on https://arxiv.org/pdf/2606.30358.