# Realizable Hamiltonians for Universal Adiabatic Quantum Computers

## TL;DR

This paper introduces two simple, practical 2-local Hamiltonian models that are proven to be universal for adiabatic quantum computation and are QMA-complete, aiding experimental realization.

## Contribution

It presents the simplest known QMA-complete 2-local Hamiltonians suitable for experimental implementation of universal adiabatic quantum computers.

## Key findings

- The 2-local Ising model with a transverse field can be made universal by adding a tunable 2-local transverse XX coupling.
- Spin models with only 1-local Z and X fields and 2-local ZX interactions are also shown to be universal and QMA-complete.

## Abstract

It has been established that local lattice spin Hamiltonians can be used for universal adiabatic quantum computation. However, the 2-local model Hamiltonians used in these proofs are general and hence do not limit the types of interactions required between spins. To address this concern, the present paper provides two simple model Hamiltonians that are of practical interest to experimentalists working towards the realization of a universal adiabatic quantum computer. The model Hamiltonians presented are the simplest known QMA-complete 2-local Hamiltonians. The 2-local Ising model with 1-local transverse field which has been realized using an array of technologies, is perhaps the simplest quantum spin model but is unlikely to be universal for adiabatic quantum computation. We demonstrate that this model can be rendered universal and QMA-complete by adding a tunable 2-local transverse XX coupling. We also show the universality and QMA-completeness of spin models with only 1-local Z and X fields and 2-local ZX interactions.