Single qubit gates by selective excitation with Jump and Return sequences

We discuss the implementation of frequency selective rotations using sequences of hard pulses and delays. These rotations are suitable for implementing single qubit gates in Nuclear Magnetic Resonance (NMR) quantum computers, but can also be used in other related implementations of quantum computing. We also derive methods for implementing hard pulses in the presence of moderate off-resonance effects, and describe a simple procedure for implementing a hard 180 degree rotation in a two spin system. Finally we show how these two approaches can be combined to produce more accurate frequency selective rotations.