Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. They will likely lead to a new wave of technological innovations in communication, computation and cryptography. As the theory of quantum physics is fundamentally stochastic, randomness and uncertainty are deeply rooted in quantum computation, quantum information and quantum simulation. Thus statistics can play an important role in quantum computation and quantum simulation, which in turn offer great potential to revolutionize computational statistics. This talk will first give a brief introduction on quantum computation and then present my recent work on quantum tomography via compressed sensing as well as statistical modeling and analysis of quantum computing experimental data.