Robust Structure Learning of k-local Lindbladians
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 a supplied weighted interaction-strength bound α̅, the protocol estimates all Hamiltonian and dissipative Pauli--GKSL coefficients with total coefficient error at each site at most ε with probability at least 1−δ using 𝒪̃k(α̅2n2k−2ε−2log(n/δ)) samples and polylogarithmically many distinct evolution times. This guarantee requires no degree, sparsity, or tail promise. A convex optimization converts these estimates into a valid k-local Lindblad generator with diamond-norm error at most ε using 𝒪̃k(α̅2n2kε−2log(n/δ)) samples and polynomial-time classical postprocessing. With a supplied local effective-sparsity bound r and a sufficiently small sitewise subthreshold tail 𝒪k(ε), coefficient recovery requires only 𝒪̃k(α̅2r2ε−2log(n/δ)) samples, without a supplied threshold or coefficient locations and without a coefficient-gap assumption. In particular, exactly sparse bounded-degree models have logarithmic sample dependence on n. We also provide guard-band support recovery and complementary supplied-candidate guarantees, extend the guarantees to model misspecification, and prove complementary sample-complexity lower bounds.
Related
- Learning Local Fermionic Lindbladians under Parity Superselection
- Semiparametric Bayesian structure learning of nonparanormal directed acyclic graphs with local--global shrinkage
- Robust Local Fréchet Regression: Nonasymptotic Theory and Minimax Optimality
- Optimal relaxation for Witten Lindbladians
- Local-discrepancy ambiguity sets for distributionally robust optimization
BibTeX
@misc{mobus2026robust,
title = {{Robust Structure Learning of $k$-local Lindbladians}},
author = {Tim Möbus and Thiago Bergamaschi and Daniel Stilck França and Cambyse Rouzé},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.23652},
eprint = {2606.23652},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.23652},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Robust Structure Learning of k-local Lindbladians
AU - Tim Möbus
AU - Thiago Bergamaschi
AU - Daniel Stilck França
AU - Cambyse Rouzé
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2606.23652
UR - https://arxiv.org/abs/2606.23652
AB - 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 a supplied weighted interaction-strength bound α̅, the protocol estimates all Hamiltonian and dissipative Pauli--GKSL coefficients with total coefficient error at each site at most ε with probability at least 1−δ using 𝒪̃_k(α̅^2n^2k−2ε^−2log(n/δ)) samples and polylogarithmically many distinct evolution times. This guarantee requires no degree, sparsity, or tail promise. A convex optimization converts these estimates into a valid k-local Lindblad generator with diamond-norm error at most ε using 𝒪̃_k(α̅^2n^2kε^−2log(n/δ)) samples and polynomial-time classical postprocessing. With a supplied local effective-sparsity bound r and a sufficiently small sitewise subthreshold tail 𝒪_k(ε), coefficient recovery requires only 𝒪̃_k(α̅^2r^2ε^−2log(n/δ)) samples, without a supplied threshold or coefficient locations and without a coefficient-gap assumption. In particular, exactly sparse bounded-degree models have logarithmic sample dependence on n. We also provide guard-band support recovery and complementary supplied-candidate guarantees, extend the guarantees to model misspecification, and prove complementary sample-complexity lower bounds.
ER -