work Combinatorial Optimization on Rydberg Atom Arrays End-to-end study of neutral-atom quantum optimization — from QUBO graph construction to error mitigation and approximation-resolved performance benchmarking. Chiral Central Charge under Entanglement Area Law Deviations How subleading corrections to the entanglement area law bias numerical extraction of c₋ in (2+1)D topological phases. Thermal Operations vs. Gibbs-Preserving Covariant Channels State reachability and catalysis-based bridging between two fundamental classes of thermodynamically consistent quantum channels. Classical Shadow Tomography for TFIM Phase Transitions Shadow-estimated Rényi-2 entropy benchmarked against exact diagonalization across the critical point of the transverse-field Ising model. fun