  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 simulation and quantum information. Consequently quantum
algorithms are random in nature, and quantum simulation utilizes Monte Carlo
techniques extensively. Thus statistics can play an important role in quantum
computation and quantum simulation, which in turn offer great potential to
revolutionize computational statistics. While only pseudo-random numbers can be
generated by classical computers, quantum computers are able to produce genuine
random numbers; quantum computers can exponentially or quadratically speed up
median evaluation, Monte Carlo integration and Markov chain simulation. This
paper gives a brief review on quantum computation, quantum simulation and
quantum information. We introduce the basic concepts of quantum computation and
quantum simulation and present quantum algorithms that are known to be much
faster than the available classic algorithms. We provide a statistical
framework for the analysis of quantum algorithms and quantum simulation.
