A quantum computer is a digital computer capable of exploiting quantum coherence among the physical two-state systems that store the binary arithmetic information.
To factor an integer is to find its (unique) expression as a product of prime numbers.
The most impressive, most important, and best-known thing a quantum computer can do is to factor with spectacular efficiency the product of two enormous prime numbers. But what on earth can quantum mechanics have to do with factoring?
This question bothered me for four years, from the time I heard about the discovery that a quantum computer was spectacularly good at factoring until I finally took the trouble to find out how it was done. The answer, you will be relieved—but, if you're like me, also a little disappointed—to learn, is that quantum mechanics has nothing at all directly to do with factoring. But it does have a lot to do...