AI summaryⓘ
The authors developed a method to learn how a quantum system with many interacting parts changes over time, focusing on interactions involving up to k qubits. Their approach only needs simple starting states, short time measurements, and single-qubit observations, without knowing the system's interaction layout beforehand. They provide guarantees on the accuracy and number of measurements needed, which scale efficiently with system size under certain conditions. They also offer ways to identify the important interactions and handle imperfect models, along with proofs showing how many measurements are fundamentally required. This work represents the first efficient learning results for such complex quantum systems with limited experimental access.
k-local Lindblad generatorquantum tomographyPauli measurementsdissipative quantum dynamicssample complexityquantum noisesemidefinite programmingdiamond normsparse learningquantum channels
Authors
Tim Möbus, Thiago Bergamaschi, Daniel Stilck França, Cambyse Rouzé
Abstract
We present an efficient protocol for learning an unknown $k$-local Lindblad generator on $n$ qubits using only product-state preparations, short-time evolution, and single-qubit Pauli measurements, without prior knowledge of the interaction structure. For fixed $k$ and bounded weighted interaction strength, the protocol estimates all Hamiltonian and dissipative Pauli--GKSL coefficients to entrywise accuracy $\varepsilon$ with probability at least $1-δ$ using $\widetilde{\mathcal O}_k(\varepsilon^{-2}n^{2k}\log(1/δ))$ samples and polylogarithmically many evolution times. A semidefinite projection converts these estimates into a valid $k$-local Lindblad generator with diamond-norm error at most $\varepsilon$ using $\widetilde{\mathcal O}_k(\varepsilon^{-2}n^{4k}\log(1/δ))$ samples and polynomial-time classical postprocessing. If a suitable set of influential coefficients is supplied and satisfies a stable sparsity condition, the dependence on $n$ can improve from polynomial to logarithmic; in particular, exact supports of bounded intersection degree require only $\widetilde{\mathcal O}_k(\varepsilon^{-2}\log(n/δ))$ samples, with analogous reductions in system-size dependence for sufficiently decaying long-range interactions. We also provide a robust structure-learning procedure, extend the guarantees to model misspecification, and prove complementary sample-complexity lower bounds. To our knowledge, these are the first efficient learning guarantees for general $k$-local dissipative quantum dynamics under such limited experimental control.