Encoding Universal Computation in the Ground States of Ising Lattices

TL;DR

This paper demonstrates how to encode universal computation within the ground states of Ising lattices, providing a new method for simulating logic gates and functions using classical 2-body interactions.

Contribution

It introduces a novel approach to encode universal computation in Ising ground states and simplifies the proof of NP-completeness for finding ground states.

Findings

Constructed simple planar Ising blocks simulating logic gates

Encoded any boolean function in Ising ground states

Revealed NP-completeness of Ising ground state problem

Abstract

We characterize the set of ground states that can be synthesized by classical 2-body Ising Hamiltonians. We then construct simple Ising planar blocks that simulates efficiently a universal set of logic gates and connections, and hence any boolean function. We therefore provide a new method of encoding universal computation in the ground states of Ising lattices, and a simpler alternative demonstration of the known fact that finding the ground state of a finite Ising spin glass model is NP complete. We relate this with our previous result about emergence properties in infinite lattices.