2026/06/22 by Tim Möbus, Thiago Bergamaschi, Daniel Stilck França +1 · 1 voice · 2 citations
Physics and Astronomy · Computer Science · Mathematics · #quant-ph #cs.IT #math.NA #math.ST
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 ε with probability at least 1-δ using \widetilde\mathcal Ok(ε-2n2klog(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 ε using \widetilde\mathcal Ok(ε-2n4klog(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 Ok(ε-2log(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.