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We demonstrate a method of exploring the quantum critical point of the Isinguniversality class using unitary maps that have recently been demonstrated inion trap quantum gates. We reverse the idea with which Feynman conceivedquantum computing, and ask whether a realisable simulation corresponds to aphysical system. We proceed to show that a specific simulation (a unitary map)is physically equivalent to a Hamiltonian that belongs to the same universalityclass as the transverse Ising Hamiltonian. We present experimental signatures,and numerical simulation for these in the six-qubit case.Comment: 12 pages, 6 figure

Fast simulation of a quantum phase transition in an ion-trap realizable unitary map