  We study three-electron-spin decoherence in a semiconductor triple quantum
dot with a linear geometry. The three electron spins are coupled by exchange
interactions J_{12} and J_{23}, and we clarify inhomogeneous and homogeneous
dephasing dynamics for a logical qubit encoded in the (S=1/2,S_{z} =1/2)
subspace. We first justify that qubit leakage via the fluctuating Overhauser
field can be effectively suppressed by sufficiently large Zeeman and exchange
splittings. For J_{12}=J_{23} and the case of J_{12} and J_{23} being
different, we construct an effective pure dephasing Hamiltonian with the Zeeman
splitting much larger than the exchange splitting. Both effective Hamiltonians
have the same order of magnitude as that for a single-spin qubit, and the
relevant dephasing time scales are of the same order as those for a single
spin. We provide estimates of the dynamics of three-spin free induction decay,
the decay of a Hahn spin echo, and the decay of echoes from a CPMG pulse
sequence for GaAs quantum dots.
