Advancements in numerical methods for quantum resources

Abstract The evolution of statistical physics from its mid-twentieth-century roots to its modern interplay with quantum information (QI) has reshaped how complex many-body systems are modeled and quantified. Classical tools now coexist with quantum-mechanical concepts like entanglement, coherence, and non-stabilizerness, which function as resources in the operational framework of quantum resource theories. As a case study, we present a recent numerical approach based on tensor cross interpolation (TCI) for computing resource measures that conceptually consolidates ideas that underlie modern computational techniques. Motivated by this, we survey numerical methods for evaluating quantum resources in many-body systems, emphasizing what scales to large sizes in practice. We organize the discussion around three families: subspace decomposition (Krylov methods, tensor networks (TNs)), stochastic sampling (Monte Carlo), and learning-based models (neural quantum states), and outline how each supports the evaluation of entanglement, non-stabilizerness (magic), and coherence. We provide a concise comparison that summarizes available measures and highlights current open problems and perspectives.