We present a reformulation of the variational quantum Monte Carlo (VQMC) method using the N-particle density matrix (N-PDM VQMC), which allows us to reduce the conventional cubic scaling behavior to linear for the calculation of the local energy with the number of electrons for systems with a nonvanishing highest occupied molecular orbital-lowest unoccupied molecular orbital gap. The perturbation of the electron distribution, caused by the truncation of the self-consistent-field (SCF) one-electron density matrix, is compensated by the use of the McWeeny purification transformation in the presented scheme. The performance and accuracy of the presented method are illustrated through exemplary calculations.
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