The Complexity of Quantum Systems on a One-dimensional Chain
Quantum Physics
2008-02-19 v2
Abstract
We prove that adiabatic computation is equivalent to standard quantum computation even when the adiabatic quantum system is restricted to be a set of particles on a one-dimensional chain. We give a construction that uses a 2-local Hamiltonian on nearest neighbors using particles that can have ten distinct states. This implies a construction of a one-dimensional chain of qubits in which the Hamiltonian is 6-local. We adapt this construction to show that the 2-local Hamiltonian for 13-state particles is QMA-complete which in turn implies that the 8-local Hamiltonian restricted to a one-dimensional chain of qubits is QMA-complete.
Keywords
Cite
@article{arxiv.0705.4067,
title = {The Complexity of Quantum Systems on a One-dimensional Chain},
author = {Sandy Irani},
journal= {arXiv preprint arXiv:0705.4067},
year = {2008}
}