Quantum gates induced by geometric phases are intrinsically robust against noise due to their global properties of the evolution paths. Compared to conventional nonadiabatic geometric quantum computation (NGQC), the recently proposed nonadiabatic noncyclic geometric quantum computation (NNGQC) works in a faster fashion, while still remaining the robust feature of the geometric operations. Here, we experimentally implement the NNGQC in a single trapped ultracold $^{40}$Ca$^{+}$ ion for verifying the noise-resilient and fast feature. By performing unitary operations under imperfect conditions, we witness the advantages of the NNGQC with measured fidelities by quantum process tomography in comparison with other two quantum gates by conventional NGQC and by straightforwardly dynamical evolution. Our results provide the first evidence confirming the possibility of accelerated quantum information processing with limited systematic errors even in the imperfect situation.
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