2025/10/22 by A. Li, Li, Alfred, Ankit Mahajan +3
Computer Science · Physics and Astronomy · #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Strongly Correlated Electrons (cond-mat.str-el) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2510.19914
openalex publication_date 2025/10/22 · openalex created_date 2025/10/25 · openalex updated_date 2026/07/28
Auxiliary-field quantum Monte Carlo (AFQMC) is typically formulated as an open-ended random walk in an overcomplete space of Slater determinants, implemented through a Langevin equation. However, the explicit form of the underlying Fokker-Planck equation governing the walker population distribution has remained unknown. In this paper, we derive the Fokker-Planck equation for AFQMC and propose a novel numerical scheme to solve it. The solution of the Fokker-Planck equation reveals the wavefunction actually sampled by the AFQMC algorithm. Interestingly, we find that even when the exact ground state is used as a guiding wavefunction in constrained path AFQMC, contrary to the common assumption, the wavefunction sampled by AFQMC is not exact. Beyond clarifying several fundamental aspects of AFQMC, the availability of a Fokker-Planck equation formulation opens new avenues for systematically improving its accuracy, which we outline in this paper.