Single-Particle Spectral Estimation
This research introduces Single-Particle Spectral Estimation (SPSE) to recover single-particle energies from a Hamiltonian. It uses a factorization of the partition function and complex contour integration over inverse fugacity to isolate energy moments. The method guarantees recovery of the true distribution within a specified Wasserstein distance, proving its feasibility for hard learning problems like DQC1-hard instances.