Motivated by the phenomenal experimental progress in the coherent control of superconducting resonators, I will describe theoretical progress in how to perform full quantum computation using these devices operating with d (>2) dimensional quantum states (qudits). This progress includes multiple routes to single-qudit logic, entangled state synthesis, and two-qudit logic gates. I will also highlight the theoretical potential and experimental challenges of this approach to quantum logic, in relation to recent work on qudit nonlocality and the quantum Fourier transform.
