Erratum to: Measuring the tilt of primordial gravitational-wave power spectrum from observations

Geometric phases are only dependent on evolution paths but independent of evolution details so that they possess some intrinsic noise-resilience features. Based on different geometric phases, various quantum gates have been proposed, such as nonadiabatic geometric gates based on nonadiabatic Abelian geometric phases and nonadiabatic holonomic gates based on nonadiabatic nonAbelian geometric phases. Up to now, nonadiabatic holonomic one-qubit gates have been experimentally demonstrated with superconducting transmons, where the three lowest levels are all utilized in operation. However, the second excited state of transmons has a relatively short coherence time, which results in a decreased fidelity of quantum gates. Here, we experimentally realize Abelian-geometric-phase-based nonadiabatic geometric one-qubit gates with a superconducting Xmon qubit. The realization is performed on the two lowest levels of an Xmon qubit and thus avoids the influence from the short coherence time of the second excited state. The experimental result indicates that the average fidelities of single-qubit gates can be up to 99.6% and 99.7% characterized by quantum process tomography and randomized benchmarking.