  We present a scalable uniform technique for construction of highly
conditional C$^n$-NOT quantum gates of trapped ion qubits, such as the Toffoli
gate, without using ancilla states and circuits of an exorbitant number of
concatenated one- and two-qubit gates. Apart from the initial dressing of the
internal qubit states with vibrational phonons and the final restoration of the
phonon ground state, our technique requires the application of just a single
composite pulse on the target qubit and is applicable both in and outside the
Lamb-Dicke regime. We design special narrowband composite pulses, which
suppress all transitions but the conditional transition of the target qubit;
moreover, these composite pulses significantly improve the spatial addressing
selectivity.
