  We describe how the spin coherence time of a localized electron spin in
solids, i.e. a solid state spin qubit, can be prolonged by applying designed
electron spin resonance pulse sequences. In particular, the spin echo decay due
to the spectral diffusion of the electron spin resonance frequency induced by
the non-Markovian temporal fluctuations of the nuclear spin flip-flop dynamics
can be strongly suppressed using multiple-pulse sequences akin to the
Carr-Purcell-Meiboom-Gill pulse sequence in nuclear magnetic resonance. Spin
coherence time can be enhanced by factors of 4-10 in GaAs quantum dot and Si:P
quantum computer architectures using composite sequences with an even number of
pulses.
