From Random Determinants to the Ground State

Abstract: Accurate quantum many-body calculations often depend on reliable reference states or good human-designed ansätze, yet these sources of knowledge can become unreliable in hard problems like strongly correlated systems. We introduce the Trimmed Configuration Interaction (TrimCI) method, a prior-knowledge-free algorithm that builds accurate ground states directly from random Slater determinants. TrimCI iteratively expands the variational space and trims away unimportant states, allowing a random initial core to self-refine into an accurate approximation of exact ground state. Across challenging benchmarks, TrimCI achieves state-of-the-art accuracy with strikingly efficiency gains of several orders of magnitude. For [4Fe-4S] cluster, it matches recent quantum computing results with $10^6$-fold fewer determinants and CPU-hours. For the nitrogenase P-cluster, it matches selected-CI accuracy using $10^5$-fold fewer determinants. For $8\times8$ Hubbard model, it recovers over $99\%$ of the ground-state energy using only $10^{-28}$ of the Hilbert space. In some regimes, TrimCI attains orders-of-magnitude higher accuracy than AFQMC method. These results demonstrate that high-accuracy many-body ground states can be discovered directly from random determinants, establishing TrimCI as a prior-knowledge-free, accurate and highly efficient framework for quantum many-body systems. The compact explicit wavefunctions it produces further enable direct and rapid evaluation of observables.