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As Feynman proposed a couple of decades ago, a well-controlled quantum system called a "quantum simulator" can efficiently simulate other interesting and complex quantum systems that are otherwise intractable. For a collection of spins subject to a fully-connected frustrated Ising interaction, current conventional computations can simulate no more than about 20-30 spins. A crystal of trapped ions system is one of most promising quantum systems for the realization of such a quantum simulator. We demonstrate the quantum simulation of a frustrated Ising Hamiltonian in a transverse field with 3 spins [1] and increase the number of spins up to 9 for the case of all ferromagnetic interactions [2]. This is an important benchmark as the system is fast approaching a level where classical simulation will not be possible. In the experiment with up to 9 spins, we observe several technical imperfections such as state detection efficiencies, spontaneous emissions, AC stark shift fluctuations, qubit decoherence of qubits, and heating of motion. We find that these errors do not appreciably affect the observation of the magnetic order while crossing a phase transition from paramagnetism to ferromagnetism as the system size increases. We finally speculate on how this system can be scaled to models that cannot be simulated using classical computers. This research was supported by the DARPA OLE program under ARO contract, IARPA through ARO contract, the NSF PIF Program, the AQUTE program, and the NSF Physics Frontier Center at JQI. [1] K. Kim, et al., Nature 465, 590 (2010). [2] In preparation

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