Superconducting artificial atoms are created by connecting Josephson junctions, which are nonlinear, non-dissipative elements, to simple electrical circuits. Individual artificial atoms can be coupled using this same toolbox of inductors, capacitors, and Josephson junctions to build novel quantum materials. In this talk, I will discuss prospects for using the fluxonium artificial atom as a building block for topological materials. Topological phases of matter have excitations with exotic quantum statistics and have been proposed as a platform for robust quantum computation. Building a topological material from the bottom-up, however, requires individual components with degenerate ground states and strong coupling between these components.
I will describe two circuits based on the fluxonium artificial atom that meet these requirements. The first circuit is an artificial molecule composed of two strongly-coupled fluxonium artificial atoms, which realizes a Hamiltonian with a dominant z z -type interaction between the individual atoms . We find excellent agreement between the measured spectroscopy of the circuit and the theoretically-predicted level transitions, which highlights the suitability of superconducting circuits for implementing tailored quantum systems. Instead of the cos x energy term characteristic of a Josephson junction, the second circuit realizes an unconventional cos 2x energy term, which results in a nearly-degenerate ground-excited state manifold. Taken together, these circuits fulfill the requirements for the building blocks of topological phases and we can thus start to realize topological materials using superconducting circuits.
 A. Kou, et al., arxiv:1610.01094 (2016).