Researchers have developed a new method, named SPICES (Single-Particle Inference via Contour Estimators), to determine the energy weights (Eᵢ) of Hamiltonians in quantum systems. This breakthrough is crucial for materials modeling, where the structure of non-interacting modes in a system is obscured by an unknown global unitary transformation (U). SPICES aims to recover these Eᵢ values without needing to reconstruct the complex U transformation, significantly simplifying the Hamiltonian learning process.

The problem of learning these Hamiltonians, even with an underlying non-interacting structure, has been shown to be DQC1-hard, indicating its computational complexity. SPICES addresses this difficulty by combining a Hadamard test, a quantum technique for phase estimation, with a novel classical post-processing procedure. This approach efficiently recovers the spectral distribution of energies in Wasserstein distance, under certain physical assumptions.

The key to the SPICES method lies in exploiting the correspondence between the single-particle energies of individual quasiparticles and the Fourier frequencies governing the zeros of the partition function at complex inverse temperature. Given that quasiparticle spectra are fundamental in downstream materials calculations, and that SPICES is a practical and straightforward method to implement, it is expected to have a significant impact on quantum materials simulations. Its application could improve the accuracy and efficiency of classical methods such as mean-field theory, Green's functions, and density functional theory.