  We propose a scheme for detecting noncommutative feature of the non-Abelian
geometric phase in circuit QED, which involves three transmon qubits
capacitively coupled to an one-dimensional transmission line resonator. By
controlling the external magnetic flux of the transmon qubits, we can obtain an
effective tripod interaction of our circuit QED setup. The noncommutative
feature of the non-Abelian geometric phase is manifested that for an initial
state undergo two specific loops in different order will result in different
final states. Our numerical calculations show that this difference can be
unambiguously detected in the proposed system.
