We present a scheme for implementing quantum operations with superconducting qubits. Our approach "coupler" qubit to mediate a controllable interaction between data qubits, pulse sequences which strongly mitigate the effects of 1/f flux noise, and a high-Q resonator-based local memory. We develop a Monte Carlo simulation technique capable of describing arbitrary noise-induced dephasing and decay, and demonstrate in this system a set of universal gate operations with O(10^-5) error probabilities in the presence of experimentally measured levels of 1=f noise. We then add relaxation and quantify the decay times required to maintain this error level.