When you learned to tie knots as a child, you probably thought their main use was for making bows on birthday presents or keeping your shoes on your feet. However, if a small band of mathematicians and physicists has its way, knots will form the basis for an entirely new kind of computer, one whose power vastly outstrips that of the machines at our disposal today.
In its first century, the mathematical study of knots belonged squarely to the realm of pure mathematics, seemingly divorced from any practical applications. In the past decade, however, mathematicians have turned knot theory into a bridge between two seemingly unconnected subjects: computer science and quantum mechanics, the branch of physics that deals with the ultrasmall scale of atoms and subatomic particles.