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The computational cost of a Monte Carlo algorithm can only be meaningfullydiscussed when taking into account the magnitude of the resulting statisticalerror. Aiming for a fixed error per particle, we study the scaling behavior ofthe diffusion Monte Carlo method for large quantum systems. We identify thecorrelation within the population of walkers as the dominant scaling factor forlarge systems. While this factor is negligible for small and medium sizedsystems that are typically studied, it ultimately shows exponential scaling.The scaling factor can be estimated straightforwardly for each specific systemand we find that is typically only becomes relevant for systems containing morethan several hundred atoms.

Diffusion Monte Carlo: Exponential scaling of computational cost for large systems