Single- and multi-qubit operations for trapped ion hyperfine or Zeeman qubits are typically implemented by continuous-wave lasers driving stimulated Raman transitions. Here we report two distinct regimes for driving these transitions with mode-locked pulsed lasers instead of cw systems. In the resolved-sideband regime, multiple pulses from a mode-locked laser constructively accumulate transition amplitude to drive the gate. In the regime where the pulse train is shorter than the oscillation period of motional modes, the mode spectrum is unresolvable and all allowed sidebands are driven simultaneously. We demonstrate a single qubit gate in about 50 ps in this regime, and discuss extensions to multi-qubit gates.