Realizable Hamiltonians for Universal Adiabatic Quantum Computers

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.

Paper revised and extended to improve clarity; to appear in Physical Review A

References in corpus (3)

• Simple proof of equivalence between adiabatic quantum computation and the circuit model
• A simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation
• Quantum annealing of the random-field Ising model by transverse ferromagnetic interactions

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• Simulation of Many-Body Hamiltonians using Perturbation Theory with Bounded-Strength Interactions
• Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State
• Quantum Computation Beyond the Circuit Model
• The Local Consistency Problem for Stoquastic and 1-D Quantum Systems