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arXiv · 1111.3291

Cavity approach to variational quantum mechanics

A. Ramezanpour
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Abstract

A local and distributive algorithm is proposed to find an optimal trial wave-function minimizing the Hamiltonian expectation in a quantum system. To this end, the quantum state of the system is connected to the Gibbs state of a classical system with the set of couplings playing the role of variational parameters. The average energy is written within the replica-symmetric approximation and the optimal parameters are obtained by a heuristic message passing algorithm based on the Bethe approximation. The performance of this approximate algorithm depends on the structure and quality of the trial wave-functions; starting from a classical system of isolated elements, i.e. mean-field approximation, and improving on that by considering the higher order many-body interactions. The method is applied to some disordered quantum Ising models in transverse fields and the results are compared with the exact ones for small systems.

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A. Ramezanpour. 2011-11-14. Cavity approach to variational quantum mechanics. https://doi.org/10.1103/physrevb.85.125131

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