Coherent quantum effects are the hallmark of atomic systems. The field of circuit quantum electrodynamics (cQED) also allows for the control of coherent quantum systems. However, these quantum states do not correspond to atomic degrees of freedom, but to the quantized behavior of the electromagnetic field in a macroscopic superconducting circuit. These ``artificial atoms" simulate many of the effects in atomic systems, with the added benefits of tunability and fast control and measurement.
This thesis explores the different artificial atoms and quantum operations accessible to us using superconducting circuits, and the techniques we can use to create more interesting and complex atoms.