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We introduce a family of Hamiltonian systems for measurement-based quantumcomputation with continuous variables. The Hamiltonians (i) are quadratic, andtherefore two body, (ii) are of short range, (iii) are frustration-free, and(iv) possess a constant energy gap proportional to the squared inverse of thesqueezing. Their ground states are the celebrated Gaussian graph states, whichare universal resources for quantum computation in the limit of infinitesqueezing. These Hamiltonians constitute the basic ingredient for the adiabaticpreparation of graph states and thus open new venues for the physicalrealization of continuous-variable quantum computing beyond the standardoptical approaches. We characterize the correlations in these systems atthermal equilibrium. In particular, we prove that the correlations across anymultipartition are contained exactly in its boundary, automatically yielding acorrelation area law.

Gapped Two-Body Hamiltonian for continuous-variable quantum computation