The notion of compressed quantum computation is employed to simulate the
Ising interaction of a 1D--chain consisting out of $n$ qubits using the
universal IBM cloud quantum computer running on $\log(n)$ qubits. The external
field parameter that controls the quantum phase transition of this model
translates into particular settings of the quantum gates that generate the
circuit. We measure the magnetization, which displays the quantum phase
transition, on a two--qubit system, which simulates a four--qubit Ising chain,
and show its agreement with the theoretical prediction within a certain error.
We also discuss the relevant point of how to assess errors when using a cloud
quantum computer. As a solution, we propose to use validating circuits, that is
to run independent controlled quantum circuits of similar complexity to the
circuit of interest.