Quantum Computing and Communication 1 Paul E. Black, D. Richard Kuhn, Carl J. Williams National Institute of Standards and Technology Gaithersburg, MD 20899 {paul.black, kuhn, carl.williams}@nist.gov Keywords: quantum computing, error correcting codes, entanglement, superposition, quantum cryptography, quantum communication, quantum information. $EVWUDFW A quantum computer, if built, will be to an ordinary computer as a hydrogen bomb is to gunpowder, at least for some types of computations. Today no quantum computer exists, beyond laboratory prototypes capable of solving only tiny problems, and many practical problems remain to be solved. Yet the theory of quantum computing has advanced significantly in the past decade, and is becoming a significant discipline in itself. This article explains the concepts and basic mathematics behind quantum computers and some of the promising approaches for building them. We also discuss quantum communication, an essential component of future quantum information processing, and quantum cryptography, widely expected to be the first practical application for quantum information technology.  ,QWURGXFWLRQ Computer users have become accustomed to an exponential increase in computing speed and capacity over the past few decades. Gordon Moore observed in 1965 that chip capacity doubled every year. Although the growth rate has slowed to “only” doubling about every 18 months, the geometric increase predicted by “Moore’s law”, as it is called, has held for over 40 years. Today’s high-end PCs have the same power as machines that were considered supercomputers not long ago. Software advances have been equally dramatic, perhaps most familiar to the average user in the form of computer graphics. The crude colored dots and flat polygons in computer games of 20 years ago have been replaced by the near-photorealistic graphics of today’s video games and movies. An enormous amount of computing power is required for the complex software used in computer animations, molecular biology analyses, computational fluid dynamics, global climate and economic modeling, worldwide credit card processing, and a host of other sophisticated applications. The demands of these problem domains have led researchers to develop distributed computing systems harnessing the power of thousands, and in 1 Preprint of article to appear in Advances in Computers, Marvin Zelkowitz, ed. Available at http://hissa.nist.gov/~black/Papers/quantumCom.html