Abstract: Quantum information processing (QIP) has been identified as one of the key future technologies that are crucial for communication, cryptography, high-performance computing, complex-system simulation, and national security. Quantum control, on the other hand, provides a powerful mathematical tool to study and analyze the QIP devices. In this talk, I will give a brief introduction to quantum control, and in particular, I will focus on our recent work that applies differential geometry to studying the quantum gate generation problems. This new framework will benefit in providing a more efficient numerical method than the traditional ones in calculating the time-optimal solution to generate the target quantum gate.