(color online) Quantum gate and its experimental implementation. (a) A single qubit quantum gate (Hadamard gate) can be understood as a rotation on the Bloch sphere. (b) The envelop of a plain pulse and (c) a shaped pulse (REBURP) in the time domain. The carrier frequency is ignored in this schematic plot. Panels (d) and (e) are the same pulses as shown in panels (b) and (c), but in frequency domain. The shaped pulse has almost equal excitation in a sharply edged region, makes it particularly suite for the selective excitations. Reproduced from Ref. [76], AIP.