Curator's Take
This article delivers the first provably efficient method for learning general k‑local Lindblad generators using only product‑state preparations, short‑time evolution and single‑qubit Pauli measurements, extending recent Hamiltonian‑learning breakthroughs to open‑system dynamics. By achieving sample complexities that scale polylogarithmically with system size under realistic sparsity or decay assumptions, it opens a practical route to characterising noise and dissipation on near‑term quantum processors—a key step for error mitigation, hardware benchmarking, and designing robust quantum algorithms. The results are grounded in rigorous diamond‑norm guarantees, though they rely on bounded interaction strengths and knowledge of the locality parameter k, so future work will need to relax these constraints for fully black‑box scenarios.
— Mark Eatherly
Summary
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.