Geometric Phases, Noise and Non-adiabatic Effects in Multi-level Superconducting Systems

Geometric phases depend neither on time nor on energy, but only on the trajectory of the quantum system in state space. In previous studies [1], we have observed them in a Cooper pair box qubit, a system with large anharmonicity. We now make use of a superconducting transmon-type qubit with low anharmonicity to study geometric phases in a multi-level system. We measure the contribution of the second excited state to the geometric phase and find very good agreement with theory treating higher levels perturbatively. Furthermore, we quantify non-adiabatic corrections by decreasing the manipulation time in order to optimize our geometric gate. Geometric phases have also been shown to be resilient against adiabatic field fluctuations [2]. Here, we analyze the effect of artificially added noise on the geometric phase for different system trajectories. \newline [1] P.~J.~Leek \emph{et al.}, \emph{Science} \textbf{318}, 1889 (2007) \newline [2] S.~Filipp \emph{et al.}, \emph{Phys.~Rev.~Lett.~}\textbf{102}, 030404 (2009)