The Complexity of Quantum Systems on a One-dimensional Chain

Details The Complexity of Quantum Systems on a One-dimensional Chain The Complexity of Quantum Systems on a One-dimensional Chain

2007-05-28

arxiv.org/abs/0705.4067v2

Physics

Quantum Physics

This paper has been merged with arXiv:0705.4077 and is now co-authored with Dorit Aharonov, Daniel Gottesman, and Julia Kempe.

Scientific paper

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.

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