Description
This monograph develops a unified theoretical framework in which quantum magic - understoodas non-stabilizer structure - emerges as a fundamental geometric and field-theoretic property of quantum systems. Moving beyond the traditional focus on entanglement, we argue that acomplete description of quantum states, especially at criticality, requires the explicit incorporationof computational resources that are inherently non-Clifford and nonlocal, and which cannot bereduced to stabilizer-based representations. We begin by formalizing the resource theory of magic, introducing mana and related monotonesas quantitative measures of deviation from stabilizer manifolds. These measures are thenreinterpreted geometrically: stabilizer states correspond to locally flat regions of state space, whilemagical states exhibit intrinsic curvature, reflecting their resistance to classical simulation. This geometric perspective enables a direct comparison between entanglement, complexity, and non-stabilizer resources, positioning magic as an independent and indispensable invariant.