We designed an algorithm for learning the coefficients of an $n$-qubit constant-local Lindbladian to an error of $\varepsilon$ with a total evolution time of $O(g d^2 \log(n) / \varepsilon^2)$, where $g$ is the single-site energy and $d$ is the (approximate) degree of the interaction graph. Although Lindbladians present new challenges not found in the special case of Hamiltonians, our algorithm achieves the suite of desiderata attained by state-of-the-art Hamiltonian learning algorithms:
- It uses non-adaptive, ancilla-free randomized Pauli measurement circuits with a time resolution of only $\Theta(1/g)$;
- It works without knowledge of the structure of the unknown Lindbladian;
- It depends on a smooth form of degree, thereby supporting the learning of quasi-local and power-law Lindbladians.
Our algorithm is a simple iterative method, where the objective function consists of Fourier coefficients of the Lindbladian restricted to few-site regions. Its analysis identifies the difficulty unique to open systems, termed "confusing" terms. When the