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arXiv · 0705.4067

The Complexity of Quantum Systems on a One-dimensional Chain

Sandy Irani
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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.

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Sandy Irani. 2008-02-19. The Complexity of Quantum Systems on a One-dimensional Chain. https://arxiv.org/abs/0705.4067

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