This very technical article carries this subtitle: "A quantum version of braids could lay the groundwork for tomorrow's computers." Here are the opening paragraphs.
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.
In a paper published last month, researchers propose that this connection between the two fields might finally enable physicists to reach a decades-long goal: to exploit quantum physics to build a computer whose performance would far surpass that of computers based on the classical physics of Isaac Newton. A quantum computer, if it is ever built, will have the power to crack the cryptographic schemes that safeguard Internet transactions and to create incredibly detailed simulations of the behavior of the universe at the tiniest scale.
California Institute of Technology physicist Alexei Kitaev and Microsoft Research mathematician Michael Freedman based their theory on physicist Edward Witten's description of a physical system that should calculate the Jones polynomial of complicated knots in the course of its regularly scheduled operations.
They nicknamed their system "a topological quantum computer." This system would encode information as space-time braids, while the Jones polynomial would be calculated instantaneously, per Witten's theory.
Freedman is reluctant to put a time frame on the construction of a topological quantum computer, but he is confident that it will happen. "If the physical world is the way we think it is, it's only a matter of time," he says.
If it is ever built, such a system would yield a range of values rather than the precise value of the Jones polynomial, but that should be sufficient to solve many problems.
For Freedman, though, there's a motivation even more compelling than the possibility of creating a powerful new computer. "I'm working on this because the mathematics is so beautiful," he says. "It's an excuse to think about the two most interesting things in the world: topology and theoretical physics."
For more details, resources and references, please read the full Science News article.
Source: Erica Klarreich, Science News, Week of Feb. 22, 2003; Vol. 163, No. 8
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