  We present protocols for dissipative entanglement of three trapped-ion qubits
and discuss a scheme that uses sympathetic cooling as the dissipation
mechanism. This scheme relies on tailored destructive interference to generate
any one of six entangled W states in a three-ion qubit space. Using a
beryllium-magnesium ion crystal as an example system, we theoretically
investigate the protocol's performance and the effects of likely error sources,
including thermal secular motion of the ion crystal, calibration imperfections,
and spontaneous photon scattering. We estimate that a fidelity of $\sim$ 98 %
may be achieved in typical trapped ion experiments with $\sim$ 1 ms interaction
time. These protocols avoid timescale hierarchies for faster preparation of
entangled states.
