Holographic quantum error-correcting codes map boundary quantum information to bulk geometry. The standard construction: stabilizer codes, which are efficiently simulable on classical computers and produce flat, featureless geometries. The entanglement structure of stabilizer codes reproduces the area-law scaling of holographic entropy but misses the state-dependent features that distinguish one geometry from another.
The paper adds magic — the non-stabilizer resource that makes quantum computation universal — to the code construction. Magic-enriched codes produce state-dependent geometries: different boundary states map to genuinely different bulk geometries, not just different states on the same geometry. The bulk metric varies with the boundary state, reproducing a key feature of actual AdS/CFT that stabilizer-based codes lack.
The magic content controls the geometry. States with zero magic (stabilizer states) produce the simplest geometry. States with maximal magic produce the most complex geometry. The geometric complexity — measured by how state-dependent the bulk metric is — correlates with the computational complexity of the boundary state. Geometry and complexity track each other through the magic parameter.
The structural claim: spacetime geometry in holography is not an entanglement phenomenon alone. Entanglement produces the topology — the connectivity of the bulk — but magic produces the geometry — the curvature, the distances, the metric. Both are necessary; neither is sufficient. The holographic dictionary requires both resources because the bulk has both topological structure (from entanglement) and geometric structure (from magic). Stabilizer codes got the topology right and the geometry wrong because they had only half the resources.