Eigenstate calculations for quantum many-body problems are challenging, especially as the system size grows large. A predominant solution is to generate random approximations to the ground state and low-lying excited states with data from Monte Carlo sampling. Although this `quantum Monte Carlo' (QMC) approach does not completely resolve the curse of dimensionality, it does push the boundaries of the largest examples scientists can handle. This tutorial introduces QMC algorithms including variational Monte Carlo (VMC) and full configuration interaction quantum Monte Carlo (FCIQMC) while using quantum spin systems to illustrate these methods.
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