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

• URL: http://arxiv.org/abs/2205.13782v1
• Date: Fri, 27 May 2022 06:36:32 GMT
• Title: Computational Characteristics of Random Field Ising Model with Long-Range Interaction
• Authors: Fangxuan Liu, L.-M. Duan
• Abstract summary: We investigate the computational random field Ising model (RFIM) with long-range interactions that decay as an inverse of distance. 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 exponents.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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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