Quantum Monte Carlo (QMC) is a class of stochastic numerical techniques used to solve quantum many-body problems by sampling configurations in Hilbert or real space according to probability distributions derived from the wavefunction or density matrix. Methods such as variational Monte Carlo, diffusion Monte Carlo, path-integral Monte Carlo, and auxiliary-field QMC enable accurate estimation of ground-state and finite-temperature properties of interacting electrons, nuclei, or spins. QMC techniques explicitly incorporate electron correlation and can achieve near-exact benchmark energies, but often face challenges such as the fermion sign problem, finite-size effects, and the need for high-quality trial wavefunctions or constrained-path approximations.
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