Christopher R. Monroe and David J. Wineland (2012 Nobel in Physics) in Scientific American:
Editor’s note (10/9/2012): We are making the text of this article freely available for 30 days because the article was cited by the Nobel Committee as a further reading in the announcement of the 2012 Nobel Prize in Physics and was also written by one of the prize winners. The full article with images, which appeared in the August 2008 issue, is available for purchase here.
Over the past several decades technological advances have dramatically boosted the speed and reliability of computers. Modern computer chips pack almost a billion transistors in a mere square inch of silicon, and in the future computer elements will shrink even more, approaching the size of individual molecules. At this level and smaller, computers may begin to look fundamentally different because their workings will be governed by quantum mechanics, the physical laws that explain the behavior of atoms and subatomic particles. The great promise of quantum computers is that they may be able to perform certain crucial tasks considerably faster than conventional computers can.
Perhaps the best known of these tasks is factoring a large number that is the product of two primes. Multiplying two primes is a simple job for computers, even if the numbers are hundreds of digits long, but the reverse process—deriving the prime factors—is so extraordinarily difficult that it has become the basis for nearly all forms of data encryption in use today, from Internetcommerce to the transmission of state secrets.
More here.