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The complexity of quantum spin systems on a two-dimensional square lattice

Roberto Oliveira·Barbara M. Terhal
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Abstract

The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantum computational class QMA, see quant-ph/0406180. In this paper we show that this important problem remains QMA-complete when the interactions of the 2-local Hamiltonian are between qubits on a two-dimensional (2-D) square lattice. Our results are partially derived with novel perturbation gadgets that employ mediator qubits which allow us to manipulate k-local interactions. As a side result, we obtain that quantum adiabatic computation using 2-local interactions restricted to a 2-D square lattice is equivalent to the circuit model of quantum computation. Our perturbation method also shows how any stabilizer space associated with a k-local stabilizer (for constant k) can be generated as an approximate ground-space of a 2-local Hamiltonian.

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Roberto Oliveira, Barbara M. Terhal. 2008-06-03. The complexity of quantum spin systems on a two-dimensional square lattice. https://arxiv.org/abs/quant-ph/0504050

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