Half-BPS states in N=4 SYM with sufficiently large dimension correspond to giant gravitons or LLM geometries in gravity. The identification of the gravity states through the measurement of the multi-pole moments of the gravity fields motivates the definition of a quantum projector identification task in associative algebras, specifically centres of symmetric group algebras. The complexity of the task depends on structural properties of the centre of the group algebra of the symmetric group of permutations of $n$ distinct objects. The structural properties are captured by a number sequence $k_*(n)$ which has been obtained computationally up to $n=80$. Based on a heuristic estimate for $k_*(n)$ at large $n$ it is shown that the quantum complexity of the task, based on standard quantum phase estimation technique in quantum computation, grows polynomially with $n$. The complexity of the state identification on the gravity side based on the measurement of the values of the classical fields and a classical Fast Fourier transform also grows polynomially with $n$. The precise rules for these classical/quantum comparisons of complexity motivated by AdS/CFT remain to be clarified and the present results for the half-BPS sector provide a concrete setting for these discussions. The talk is based on the paper "The quantum detection of projectors in finite-dimensional algebras and holography" (e-Print: 2303.12154 [quant-ph] and JHEP 05 (2023) 191 ) with Joseph Bengeloun and draws on several earlier papers on AdS/CFT as well as standard texts on quantum information.