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arXiv · 2205.13782

Computational Characteristics of Random Field Ising Model with Long-Range Interaction

Fangxuan Liu·L. -M. Duan
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Abstract

Ising model is a widely studied class of models in quantum computation. In this paper we investigate the computational characteristics of the random field Ising model (RFIM) with long-range interactions that decays as an inverse polynomial of distance, which can be achieved in current ion trap system. We prove that for an RFIM with long-range interaction embedded on a 2-dimensional plane, solving its ground state is NP-complete for all diminishing exponent, and prove that the 1-dimensional RFIM with long-range interaction can be efficiently approximated when the interaction decays fast enough.

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Fangxuan Liu, L. -M. Duan. 2022-05-27. Computational Characteristics of Random Field Ising Model with Long-Range Interaction. https://doi.org/10.1103/physreva.108.012415

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