First of all, welcome and greetings to Cerebelly. Always great to have new members who share a keen interest in this kind of stuff!
I am certainly no expert in quantum computing, but I'll give it my best shot. Meanwhile, the following article is a little old (5 years), but seems to be pretty well written from the standpoint of comparing classical computing to quantum computing:
http://www.theglobalintelligencer.com/jun2007/scitechAs I understand it, the nature of the qubit, having superposition states, allows a certain class of problems that can be solved using parallel processing methods to be solved fastest using quantum computing. So, for example, let's say that there is a solution to a complex problem, say in cryptography, that would be solved in the following way on a classical machine: try a solution, see if it works - try another solution, see if it works - try another solution, see if it works, etc. Clearly the linear approach to something that requires a huge number of tries can get cumbersome on a sequential machine.
However, the way quantum process work is different. Let's say the question is "what's the next state of a system, given the current state, some random processes, and some rules about how those random processes are likely to work. For example, if the random processes are a dozen people's free will decisions, then if we know the likelihood that each person will behave in a certain way, we could imagine all of the possible combinations of how those people would behave and what each of those possibilities would mean in terms of deciding the next state. The probability wave function would be this complex thing with peaks and valleys, the peaks representing the cases of higher probability of occurring. When that next state actually happens, the wave function "collapses", meaning it is no longer probabilities, it has actually become "actualized." If the rules are pretty good, the wave functions highest peak will mostly likely be the one that becomes actualized.
So, in the cryptography example above, there is only one right solution, so the wave function would be flat except for a single peak (spike). It would be obvious what the solution is from looking at it. Quantum computing, by including these superposition states in the qubit, can solve these kinds of problems quickly by doing this massively parallel processing.
However, they are probably not very good at solving problems that have a lot of sequential characteristics to them. For example, a war simulation probably has a ton of if-then-else steps to it. If this commander makes this decision, then the opposing side could respond this way or that way, which would result in the first side doing this or that, etc. I guess a quantum computer could maybe map each step of the sequence to a qubit, but if the options are more than binary, this wouldn't work. In any case, it seems that there are still lots of computing problems for which a massively parallel approach doesn't really help. So, while the quantum computers keep getting faster and faster at solving a certain class of problems, they wouldn't necessarily make any program toward solving the other classes of problems.
Other thoughts?
