00946635 - Andrew Glassner's Notebook...

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T he computers we use today are engineering and technical marvels. They employ powerful mathe- matical abstractions about information and computa- tion to create virtual machines that can do everything from simulating a thunderstorm to engaging you in real-time battle with a Fre-breathing dragon. But for all their power, today’s computers can only do one thing at a time. Sure, we can put two computers side by side and carry out out parallel computing , but to have N streams of parallel computation, we need to have N computers. And parallel computing is hard to do efF- ciently: if we double the number of processors, the speed of computation goes up, but very rarely by a factor of 2. These are the realities of classical computing . There’s a whole new approach on the horizon, called quantum computing . The idea is to harness some of the strange properties from the world of quantum physics to build a new breed of computers. The scientiFc and engineering challenges to building a real quantum com- puter are formidable. But tiny, 3-bit quantum comput- ers have been built and they prove that the theory works. In the last issue, I introduced some of the ideas of quantum computing. Here I’ll begin with a quick recap of those ideas, and then dig into the notation and ter- minology. In the next issue we’ll see some tools and algo- rithms central to quantum computing. You’ll probably Fnd the notation here a little unusu- al, but basically all we’ll be doing is manipulating vectors and matrices. I’ll use physics language and symbology here because it’s the language of quantum computing. A quick review As a quick refresher, let’s look at the characteristics of the quantum world I discussed last time. Then I’ll quick- ly review some linear algebra, because we’ll be talking about familiar ideas with unfamiliar notation. In the following, electrons and photons are typical examples of quantum particles: n A quantum particle can exist simultaneously in many incompatible configurations, or states . We call this superposition . n We can operate on a quantum particle while it’s in a superimposed state and affect all the states at once. n When we observe a quantum particle, the very act of observation causes the particle to take on one and only one state. If we repeat the same observation before otherwise affecting the particle, we’ll see the same state. n The particle and the measuring apparatus determine the possible states that result from a measurement. As we saw last time, quantum mechanics often con- tradicts our intuition. After all, how can a particle exist simultaneously in several incompatible states? What could that possibly mean? Nothing in our everyday experience works like that—a bird is flying or it isn’t, a tree is alive or dead, and a bit is one or zero. Certainly a tree can be thriving or dying, but it can’t be alive and dead simulaneously. But in the quantum realm it’s a different story, and that opens the door to quantum computing.
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This note was uploaded on 04/10/2008 for the course ECE 2074 taught by Professor Stilwell during the Fall '08 term at Virginia Tech.

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00946635 - Andrew Glassner's Notebook...

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