Exploring Quantum Resource Landscape Through a Unified Tensor Network Framework for Entanglement and Magic Analysis

Entanglement and magic are complementary quantum resources that jointly define the computational potential of quantum systems. The resource characterization of states, in terms of their bipartite entanglement and magic structure, reveals valuable insights across domains ranging from holography in high-energy physics to quantum networks and sensing. In this talk we propose a unified framework for analyzing magic and entanglement, as well as the dynamics of both resources, in large Hilbert spaces using a hybrid tensor network and quantum circuit framework. Building on this foundation, we further employ a machine learning protocol to generate states with targeted resource profiles, and design quantum circuits to prepare these states with reduced overhead. Our approach provides a window into the geometry of the entanglement-magic phase space, offering insights into physical phenomena such as entanglement and magic driven phase transitions, quantifying the entangling power and magic-generating capabilities of operators, and ultimately clarifying the limits of quantum computation and genuine quantum advantage within the resource landscape.