n the Fixed-Node Importance-Sampling Quantum Monte Carlo Method: Performance Analysis on Model Systems
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Performance of Importance-Sampling Quantum Monte Carlo process is considered on simple, model systems, such as: multi-dimensional oscillator, hydrogen-like ions, and "helium oscillator" (quadratic-potential analog of helium atom). A mean and standard deviation of that process is numerically determined and also, in the first two cases, calculated analytically together with the distribution of the process values. Results are presented to show how a mean value precision and necessary computational time depend on an importance function quality and dimensionality of the case. Distributions are shown to be highly asymmetrical which questions the value of variance-based estimators of precision. However, a variance is proposed to be the good estimate of the importance function quality. Finally, effects of fixed-node approximation on the second excited state of oscillator are presented to explain the meaning of the differences between exact and approximate solutions.
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