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Journal of Physics A Mathematical and General

On the nodal structure of atomic eigenfunctions

Maria Hoffmann-Ostenhof, Thomas Hoffmann-Ostenhof, Barry Simon A

Published Apr 1, 1980• 7 citations
Publisher

Abstract

In an arbitrarily small neighbourhood of any zero of a real-valued bounded continuous atomic wavefunction, the wavefunction has both signs.
DOI
10.1088/0305-4470/13/4/010

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It is shown that a class of separately frustration-free (SFF) Hamiltonians can be Monte Carlo simulated efficiently on a classical computing machine, because such an SFF Hamiltonian corresponds to a Gibbs wavefunction whose nodal structure is efficiently computable by solving a small subsystem associated with a low-dimensional configuration subspace. It is further demonstrated that SFF Hamiltonians can be designed to implement universal ground state quantum computation. The two results combined have effectively solved the notorious sign problem in Monte Carlo simulations, and proved that all bounded-error quantum polynomial time algorithms admit bounded-error probabilistic polynomial time simulations.
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