  In this paper, we explore how to constructively manipulate qubits by rotating
Bloch spheres. It is revealed that three-rotation and one-rotation Hamiltonian
controls can be constructed to steer qubits when two tunable Hamiltonian
controls are available. It is demonstrated in this research that local-wave
function controls such as Bang-Bang, triangle-function and quadratic function
controls can be utilized to manipulate quantum states on the Bloch sphere. A
new kind of time-energy performance index is proposed to trade-off time and
energy resource cost, in which control magnitudes are optimized in terms of
this kind of performance. It is further exemplified that this idea can be
generalized to manipulate encoded qubits on the controllable subspace.
