The complexity of quantum spin systems on a two-dimensional square lattice
作者： Barbara M. Terhal , Roberto Oliveira
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摘要: The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantumcomputational class QMA [1]. In this paper we show that important problemremains QMA-complete when interactions of 2-local Hamiltonian are betweenqubits on a two-dimensional (2-D) square lattice. Our results partially derived withnovel perturbation gadgets employ mediator qubits which allow us manipulatek-local interactions. As side result, obtain quantum adiabatic computationusing restricted 2-D lattice is equivalent circuitmodel computation. method also shows how any stabilizerspace associated with k-local stabilizer (for constant k) can generated as anapproximate ground-space Hamiltonian.
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