The key to a quantum algorithm is getting wrong answers to cancel out (opposing complex amplitudes) and right answers to build up (harmonizing complex amplitudes). Exploring all branches simultaneously is easy. The hard part is getting the evolution of a linear, unitary quantum process to make "wrong" configuration amplitudes cancel and "correct" configuration amplitudes add. Peter Shor's critical insight in the quantum-factoring algorithm had something to do with the circularity of something to do with factors (I don't know the details).