Lindbladian reverse engineering for general non-equilibrium steady states: A scalable null-space approach, by Leonardo da Silva Souza, Fernando Iemini
Summarize this article with:
SciPost Physics Home Authoring Refereeing Submit a manuscript About Lindbladian reverse engineering for general non-equilibrium steady states: A scalable null-space approach Leonardo da Silva Souza, Fernando Iemini SciPost Phys. 20, 009 (2026) · published 16 January 2026 doi: 10.21468/SciPostPhys.20.1.009 pdf BiBTeX RIS Submissions/Reports Abstract The study of open system dynamics is of paramount importance both from its fundamental aspects as well as from its potential applications in quantum technologies. In the simpler and most commonly studied case, the dynamics of the system can be described by a Lindblad master equation. However, identifying the Lindbladian that leads to general non-equilibrium steady states (NESS) is usually a non-trivial and challenging task. Here we introduce a method for reconstructing the corresponding Lindbladian master equation given any target NESS, i.e., a Lindbladian Reverse Engineering ($\mathcal{L}$RE) approach. The method maps the reconstruction task to a simple linear problem. Specifically, to the diagonalization of a correlation matrix whose elements are NESS observables and whose size scales linearly (at most quadratically) with the number of terms in the Hamiltonian (Lindblad jump operator) ansatz. The kernel (null-space) of the correlation matrix corresponds to Lindbladian solutions. Moreover, the map defines an iff condition for $\mathcal{L}$RE, which works as both a necessary and a sufficient condition; thus, it not only defines, if possible, Lindbladian evolutions leading to the target NESS, but also determines the feasibility of such evolutions in a proposed setup. We illustrate the method in different systems, ranging from bosonic Gaussian systems, dissipative-driven collective spins and random local spin models. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.1.009TI - Lindbladian reverse engineering for general non-equilibrium steady states: A scalable null-space approachPY - 2026/01/16UR - https://scipost.org/SciPostPhys.20.1.009JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 1SP - 009A1 - da Silva Souza, LeonardoAU - Iemini, FernandoAB - The study of open system dynamics is of paramount importance both from its fundamental aspects as well as from its potential applications in quantum technologies. In the simpler and most commonly studied case, the dynamics of the system can be described by a Lindblad master equation. However, identifying the Lindbladian that leads to general non-equilibrium steady states (NESS) is usually a non-trivial and challenging task. Here we introduce a method for reconstructing the corresponding Lindbladian master equation given any target NESS, i.e., a Lindbladian Reverse Engineering ($\mathcal{L}$RE) approach. The method maps the reconstruction task to a simple linear problem. Specifically, to the diagonalization of a correlation matrix whose elements are NESS observables and whose size scales linearly (at most quadratically) with the number of terms in the Hamiltonian (Lindblad jump operator) ansatz. The kernel (null-space) of the correlation matrix corresponds to Lindbladian solutions. Moreover, the map defines an iff condition for $\mathcal{L}$RE, which works as both a necessary and a sufficient condition; thus, it not only defines, if possible, Lindbladian evolutions leading to the target NESS, but also determines the feasibility of such evolutions in a proposed setup. We illustrate the method in different systems, ranging from bosonic Gaussian systems, dissipative-driven collective spins and random local spin models.ER - × @Article{10.21468/SciPostPhys.20.1.009, title={{Lindbladian reverse engineering for general non-equilibrium steady states: A scalable null-space approach}}, author={Leonardo da Silva Souza and Fernando Iemini}, journal={SciPost Phys.}, volume={20}, pages={009}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.1.009}, url={https://scipost.org/10.21468/SciPostPhys.20.1.009},} Ontology / Topics See full Ontology or Topics database. Open quantum systems Authors / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 2 Leonardo da Silva Souza, 1 Fernando Iemini 1 Universidade Federal Fluminense / Fluminense Federal University [UFF] 2 Instituto Federal de Educação, Ciência e Tecnologia de Mato Grosso / Instituto Federal de Educação, Ciência e Tecnologia de Mato Grosso [IFMT] Funders for the research work leading to this publication Conselho Nacional de Desenvolvimento Científico e Tecnológico / National Council for Scientific and Technological Development [CNPq] Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro [FAPERJ] Instituto Serrapilheira