A measurement-based quantum computer could consist of a local-gapped Hamiltonian system, whose thermal states --at sufficiently low temperature-- are universal resources for the computation. Initialization of the computer would correspond to cooling the system. We perform an experimental quantum simulation of such cooling process with entangled photons. We prepare three-qubit thermal cluster states exploiting the equivalence between local dephasing and thermalisation for these states. This allows us to tune the systems temperature by changing the dephasing strength. We monitor the entanglement as the system cools down and observe the transitions from separability to bound entanglement, and then to free entanglement. We also analyze the performance of the system for measurement-based single-qubit state preparation. These studies constitute a basic characterisation of experimental cluster-state computation under imperfect conditions.
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