Quantum Computers 
[Oct. 2nd, 200610:13 pm]
Mysteries and Paranormal in Michigan and elsewhere

"In quantum mechanics, the state of a physical system (such as an electron or a photon) is described by a vector in a mathematical object called a Hilbert space. The realization of the Hilbert space depends on the particular system. For instance, in the case of a single particle system in three dimensions, the state can be described by a complexvalued function defined on R3 (threedimensional space) called a wave function. As described in the article on quantum mechanics, this function has a probabilistic interpretation; of particular significance is that quantum states can be in a superposition of the basis states. The time evolution of the system state vector is assumed to be unitary, meaning that it is reversible.
A classical computer has a memory made up of bits, where each bit holds either a one or a zero. The device computes by manipulating those bits, i.e. by transporting these bits from memory to (possibly a suite of) logic gates and back. A quantum computer maintains a set of qubits. A qubit can hold a one, or a zero, or a superposition of these. A quantum computer operates by manipulating those qubits, i.e. by transporting these bits from memory to (possibly a suite of) quantum logic gates and back.
Qubits for a quantum computer can be implemented using particles with two spin states: "up" and "down" (typically written 0\rangle and 1\rangle) in fact, any system possessing an observable quantity A which is conserved under time evolution and such that A has at least two discrete and sufficiently spaced consecutive eigenvalues, is a suitable candidate for implementing a qubit, since any such system can be mapped onto an effective spin1/2."

If that lost you, it lost me too. The best information I can give on this is from a class I had taken on encryption. It was explained to me that a quantum computer would completely exclude 3rd party information hackers because information would be sent directly from person to person without any sort of traveling. There would be no way to intercept the message. It had something to do with light speed and information traveling with photons. Another thing the computer is supposed to do is determine special numbers that are created by multiplying two prime numbers together. This is challenging for current computers because there is no algorithm (or pattern) of finding prime numbers like 1, 2, 3, 5, 7, 11, 13, etc. The only way current computers can solve this is to try each prime one by one until they find it. When you have a number like 29845724529363992837453, I can see why it would take a while to figure out which two primes are factors.
Here's what I just said in fancy science talk: "Integer factorization is believed to be computationally infeasible with an ordinary computer for large numbers that are the product of two prime numbers of roughly equal size (e.g., products of two 300digit primes). By comparison, a quantum computer could solve this problem relatively easily. If a number has n bits (is n digits long when written in the binary numeral system), then a quantum computer with just over 2n qubits can use Shor's algorithm to find its factors. It can also solve a related problem called the discrete logarithm problem. This ability would allow a quantum computer to "break" many of the cryptographic systems in use today, in the sense that there would be a relatively fast (polynomial time in n) algorithm for solving the problem."

More info about the power of these computers: "...some modern simulations that are taking IBM's Blue Gene supercomputer years would only take a quantum computer a matter of seconds."
I assume that's one of the fastest computers in the world. Sounds a bit faster.
As always, wikipedia strikes again. 

