Learning the structure of open quantum systems

This paper introduces a novel algorithm for structure learning of open quantum systems, specifically those governed by local Lindbladians. While Hamiltonian learning (closed systems) is well-studied, learning the dissipative dynamics of open systems (Lindbladians) presents unique challenges, such as the lack of reversible time evolution and the emergence of "confusing" terms that complicate parameter estimation. The authors overcome these hurdles by using a simple iterative method based on local Fourier coefficients and convex optimization.

The algorithm uses non-adaptive, ancilla-free randomized Pauli measurements to estimate local Fourier coefficients of the Lindbladian's time evolution. By identifying and quantifying the "confusion" caused by dissipative terms, the authors develop a robust iterative update rule that effectively filters out small, irrelevant interactions. This allows the algorithm to learn the structure of the Lindbladian—identifying which coefficients are significant—without prior knowledge of the interaction graph.

This work provides a unified framework that matches state-of-the-art performance for Hamiltonian learning while extending these capabilities to the more general and physically relevant class of Lindbladians. Beyond its primary contribution, the framework simplifies existing Hamiltonian learning algorithms and provides the first provably efficient method for learning Hamiltonian structures from high-temperature Gibbs states. These results are particularly timely given the growing interest in using Lindbladian dynamics for quantum Gibbs state preparation.

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