ABSTRACT
This chapter sketches the foundations of the subject, discussing salient features of quantum information, formulates a mathematical model of quantum computation and highlights some implications of the model. It reviews two particularly promising applications of quantum computing foreseen by Feynman, simulating the dynamics of complex quantum systems, and computing their static properties. The chapter explains the concept of quantum error correction, the basis of belief that quantum computers can be scaled up to large systems that solve very hard problems. Shor's discovery, and its obvious implications for cryptanalysis, caused interest in quantum computing to skyrocket. Because of Shor's algorithm, the public key cryptographic protocols the people use to protect privacy when they communicate over the Internet will become vulnerable to attacks by quantum computers in the future. Classical computers are especially bad at simulating quantum dynamics – that is, predicting how a highly entangled quantum state will change with time.
