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\title{Spin Coherence Excitation\\ in Pr$^{3+}$:Y$_2$SiO$_5$}
\author{Master's Thesis\\
by\\
Fredrik Vestin\\\\
Lund Reports on Atomic Physics, LRAP-297\\
Lund, February 2003
}
\date{} % Blir dagens datum om det utelämnas

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\chapter{Quantum Computers}
As classical computers are reaching their limit of performance, quantum computers are merely
taking form. Richard Feynman presented the first ideas of quantum computing 20 years ago.
Ideas that have been continuosly developed since then. Lots of thick books on quantum
information processing have been written. Even though noone has been able to build a quantum
computer and sinceneraly noone is even close.

So what is a quantum computer and how is it different from a normal computer?

Information in a normal computer is stored in bits, either 1 or 0. A register of n-bits can then store one of 2$^n$ possible configurations. Information in a quantum computer is stored
in qubits. The qubit is choosen to be a quantum system that consists of two states. Usually
denoted $\ket{0}$ and $\ket{1}$. A quantum system can be in a superposition. Meaning that
it can be in the $\ket{0}$ and the $\ket{1}$ state at the same time. A register of n-qubits
can then store all 2$^n$ configurations at the same time. This register can be used as one single input for a function. This is called quantum parallellism. A normal computer would have to do 2$^{n}$ computations or have 2$^{n}$ processors working in parallell.

Two qubits can also be in a so called entangled state. Meaning that whatever happen to one
qubit will affect the other. Even if they do not interact with each other at the moment.

Superposition and entanglement are what make a quantum cmputer and a classical computer fundamentally different from each other. These almost magical properties of a quantum computer seem to offer an enormous gain. However if you measure the content of a register you will only get one answer. Since the quantum system is said to collapse.

But there is a few proposed algorithms that would amke use of the quantum parallellism. I
won't go through them. But I think the most interesting application will be its ability to
simulate other quantum systems, which is not feasible on a normal computer.
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