Classical Identification of Emergent Geometries in AdS Spacetimes and Quantum Projector Detection

Explore a 38-minute conference talk from the Workshop on "Large-N Matrix Models and Emergent Geometry" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the correspondence between half-BPS states in N=4 SYM and giant gravitons or LLM geometries in gravity. Examine the quantum projector identification task in associative algebras, focusing on the centres of symmetric group algebras. Investigate the complexity of this task based on the structural properties of the group algebra's centre, captured by the number sequence k*(n). Learn about the polynomial growth of quantum complexity using standard quantum phase estimation techniques, and compare it to the classical complexity of state identification in gravity. Gain insights into the implications for AdS/CFT correspondence and the challenges in establishing precise rules for classical/quantum complexity comparisons. Explore the half-BPS sector as a concrete setting for these discussions, drawing from the paper "The quantum detection of projectors in finite-dimensional algebras and holography" and related works on AdS/CFT and quantum information.