Experimental realization of noncyclic geometric gates with shortcut to adiabaticity in a superconducting circuit

Possessing the noise-resilience feature, geometric phases have become important in robust quantum computation. Gates based on the Abelian and non-Abelian geometric phases have been experimentally demonstrated in different physical systems. However, previous proposals require cyclic evolution with a constant operation time even for small rotation angles, which set a limit to the gate operation time. Here, we experimentally realize noncyclic geometric gates, where the cyclic condition is removed and the operation time is proportional to the rotation angle. With the adiabatic process sped up by shortcut to adiabaticity, the fidelities of a noncyclic geometric gate characterized by randomized benchmarking are above 99.5%. Comparing with the dynamic scheme, we demonstrate the robustness of our gate against control instability in the experiment. Moreover, our results indicate that the noncyclic geometric gate with a smaller rotation angle corresponds to a shorter evolution time and higher fidelity. As small rotation angles are essential in the quantum algorithm, the superiority of noncyclic geometric gates makes them promising candidates in fast and robust quantum computation.