Quantum Computers: what are they better at?

Can someone explain to me what sort of things quantum computers can/could do, based on their differences in their design, that are harder for conventional computers?

So far I have a list that consists of 1) integer factorisation.

I was hoping someone could extend that for me! :-) After all there are operating QC right now, so someone must be using them for something.

Edit: You can get technical, if it's related to programming. QM, maybe not so :-) I have experience with software engineering that at a level that would qualify as commercial competence though I don't do it for a living.

They are 100 times faster, remember computers work by reading 0s and 1s, physically those 0s and 1s are represented with switches (transistors).
Quantum computers use the properties of quantum mechanics (a very very small world)
to treat data, so it is faster than turning a switch on and off

I'm not a physicist so I'm not able to paint the complete picture, but they are a lot faster and I guess they will be used for cloud computing.

chiro
Uhh ruben94, that's not the point of a quantum computer.

To rorix_bw, the best way to think of the benefits of a quantum computer is that this computer works on the space of evaluating 2^N functions where N is the number of qu-bits used in the quantum computer.

From the evaluation we get probabilities associated with each state and the idea is to transform these probabilities in a way physically to something that finally collapses to a result that is in-line with the computation required.

In a conventional computer: we have to perform the computation based on a given algorithmic description and the computer evaluates it.

In a quantum computer, because of the superpositions of states, everything is evaluated (corresponding to our 2^N part), and the key is to then to transform the probabilities in a way that will give the result we are looking for.

Of course we have to deal with the inputs to the quantum computer, the transformation of probabilities that correspond with the actual algorithm/computation we are making, and then how all of these things affect the collapse of the result.

But apart from that we have to deal with the physical side of decoherence and the unpredictability and difficulty to control these kinds of systems which is the real major challenge currently for QC design (especially for large systems of qu-bits).

Remember: the key thing is the super-positions of states, how these correspond to probabilities, and how both of these are exploited to do computation in a general manner that is more powerful than the standard computational paradigm.

Quantum computers are theoretically useful for NP-hard combinatorial optimization problems such as the "Traveling Salesman" where you try to figure out the shortest route to cover all the sales territory.