Resumen: We demonstrate that stationary localized solutions (discrete solitons) exist in one-dimensional Bose-Hubbard lattices with gain and loss in a semiclassical regime. Stationary solutions, by definition, are robust and do not demand state preparation. Losses, unavoidable in experiments, are not a drawback, but a necessary ingredient for these modes to exist. The semiclassical calculations are complemented with their classical limit and dynamics based on a Gutzwiller ansatz. We argue that circuit quantum electrodynamic architectures are ideal platforms for realizing the physics developed here. Finally, within the input-output formalism, we explain how to experimentally access the different phases, including the solitons, of the chain. Idioma: Inglés DOI: 10.1103/PhysRevA.91.033823 Año: 2015 Publicado en: Physical review. A, Atomic, molecular, and optical physics 91, 3 (2015), 033823 [10 pp] ISSN: 1050-2947 Factor impacto JCR: 2.765 (2015) Categ. JCR: OPTICS rank: 17 / 91 = 0.187 (2015) - Q1 - T1 Categ. JCR: PHYSICS, ATOMIC, MOLECULAR & CHEMICAL rank: 12 / 35 = 0.343 (2015) - Q2 - T2 Factor impacto SCIMAGO: 1.747 - Atomic and Molecular Physics, and Optics (Q1)