  Efficient Boltzmann-sampling using first-principles methods is challenging
for extended systems due to the steep scaling of electronic structure methods
with the system size. Stochastic approaches provide a gentler system-size
dependency at the cost of introducing "noisy" forces, which serve to limit the
efficiency of the sampling. In the first-order Langevin dynamics (FOLD),
efficient sampling is achievable by combining a well-chosen preconditioning
matrix S with a time-step-bias-mitigating propagator (Mazzola et al., Phys.
Rev. Lett., 118, 015703 (2017)). However, when forces are noisy, S is set equal
to the force-covariance matrix, a procedure which severely limits the
efficiency and the stability of the sampling. Here, we develop a new, general,
optimal, and stable sampling approach for FOLD under noisy forces. We apply it
for silicon nanocrystals treated with stochastic density functional theory and
show efficiency improvements by an order-of-magnitude.
