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A common strategy to measure the Abelian geometric phase for a qubit is to let it evolve along an orange-slice-shaped path connecting two antipodal points on the Bloch sphere by two different semi-great-circles. Since the dynamical phases vanish for such paths, this allows for direct measurement of the geometric phase. Here, we generalize the “orange-slice” setting to the non-Abelian case. The proposed method to measure the non-Abelian geometric phase can be implemented in a cyclic chain of four qubits with controllable interactions.