  We present a solid-state implementation of ultrafast conditional quantum
gates. Our proposal for a quantum-computing device is based on the spin degrees
of freedom of electrons confined in semiconductor quantum dots, thus benefiting
from relatively long decoherence times. More specifically, combining Pauli
blocking effects with properly tailored ultrafast laser pulses, we are able to
obtain sub-picosecond spin-dependent switching of the Coulomb interaction,
which is the essence of our conditional phase-gate proposal. This allows us to
realize {\it a fast two qubit gate which does not translate into fast
decoherence times} and paves the road for an all-optical spin-based quantum
computer.
