  We use analytical and numerical calculations to obtain speed limits for
various unitary quantum operations in multiqubit systems under typical
experimental conditions. The operations that we consider include single-, two-,
and three-qubit gates, as well as quantum-state transfer in a chain of qubits.
We find in particular that simple methods for implementing two-qubit gates
generally provide the fastest possible implementations of these gates. We also
find that the three-qubit Toffoli gate time varies greatly depending on the
type of interactions and the system's geometry, taking only slightly longer
than a two-qubit controlled-NOT (CNOT) gate for a triangle geometry. The speed
limit for quantum-state transfer across a qubit chain is set by the maximum
spin-wave speed in the chain.
