Effective \boldmath$\cos n \varphi$ Josephson element

Using superinductances, one can realize circuit elements with tunneling energies proportional to $\cos n \varphi$, with $\varphi$ being the phase across the element and $n$ being a positive integer. In these elements, Cooper pairs are only able to tunnel in multiples of $n$, resulting in an $n$-fold degenerate ground state manifold that can encode a qubit. Such a qubit is expected to be insensitive to most relevant noise sources [1,2]. We present the experimental realization of a qubit based on the $\cos 2 \varphi$ element and show preliminary measurements of its energy levels. \\[] [1] P. Brooks et al. Phys. Rev. A 87, 052306 (2013). \\[-1pt] [2] M.T. Bell et al. Phys. Rev. Lett. 112, 167001 (2014).