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As a test case for solving the quantum Monte Carlo sign problem, we propose an exact and stable algorithm for few-electron systems. The energies of an excited state of He and of the ground states of Li and Be are determined. We use equal numbers of positive and negative walkers, sampling new positions from a distribution that couples all walkers using a Green's function of known form. For long-term stability, the importance functions are different for positive and negative walkers. A novel transformation of the potential facilitates the evaluation of the energy.
Zhang et al. (Mon,) studied this question.