Variational Monte Carlo estimates quantum observables by sampling from parameterized wave functions. When the wave function has nodes — zeros where it changes sign — the stochastic estimators develop heavy tails with potentially divergent variances. In continuous systems, the node crossings create singularities in local estimators. In discrete systems, the sampling distribution can miss parts of the Hilbert space needed for unbiased estimates. Both pathologies wreck optimization trajectories and time-dependent dynamics.
This paper introduces blurred sampling: instead of sampling at exactly the point the walker sits, blur the sampling over a neighborhood. The blurring smooths the singularities near nodes in continuous space and fills the coverage gaps in discrete space. The method is a post-processing step — it doesn't modify the underlying sampler and incurs minimal overhead.
The rigor matters: blurred sampling has provably well-behaved estimators (finite variance, unbiased in the zero-blur limit) while standard sampling is provably pathological near nodes. The framework applies to both stochastic reconfiguration (optimization) and time-dependent VMC (dynamics). Demonstrations on representative problems where standard sampling fails show reliable convergence, and large-scale spin dynamics applications confirm scalability. The fix is adding deliberate imprecision — accepting that the exact local value at a node is informationally useless and averaging over its neighborhood instead.