We demonstrate a universal set of quantum gates on one and two trapped ions with a narrow linwidth (< 80 Hz) diode laser system. We demonstrate initialization and detection of a superposition of two Zeeman-split electronic spin states with an average error of 1.1 (1) 10^-3. This high detection fidelity allows us to demonstrate Process tomography of the null operation with a similar error. We further use this laser to perform high fidelity rotations of a superposition of two states of the narrow transition, and entanglement gates between two trapped ions. We will discuss the advantages and difficulties involved in using a diode laser system to this end.