Computational characteristics of the random-field Ising model with long-range interaction
Fangxuan Liu, L.-M. Duan · Physical Review A · 2023
The 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 the current ion trap system. We prove that for an RFIM with long-range interaction embedded on a two-dimensional plane, solving its ground state is NP-complete for all diminishing exponents, and prove that the one-dimensional RFIM with long-range interaction can be efficiently approximated when the interaction decays fast enough.