Quantum computers will take over way before 2100. Even though at the moment they are still in the secondary research state they are simply too good to ignore.
If you ignore Moore's Law for a moment, then transistors are linear. If you want a computer to run twice as fast you need twice as many bits or transistors (in reality, more like x2.5 due to inefficiencies in rerouteing calculations). Moore's Law states that every 18 months you double the number of transistors on a given chip, so every 18 months a computer doubles in speed.
Quantum computers, on the other hand, are exponential. Due to complicated physics and the fact that they do everything in parallel, adding an extra qubit (quantum equivalent of a bit) to a quantum computer doubles its speed. (In reality its more likely to be 6-12 qubits needed due to even more complicated physics). But what that means is that once they take off, quantum computers really take off. If you go from a 100 qubit to a 200 qubit quantum computer you did make it run twice as fast, you make it run over 1000 times faster. If you go from a 200 qubit to a 400 qubit qumpter (can we coin this as a new term for a quantum computer?) you make it run a million times faster.
If you say that a Moore's Law type of relationships exists for qubits as well as transistors; then what you get is that every 18 months the number of operations a computer can do squares. That is a ridiculously massively huge rate of increase. Once they take off, quantum computers really take off.
Not only that but for some specific tasks, quantum computers require less steps than a normal computer would. For example, database mining or (famously) breaking certain types of encryption. But even if qumputers require more steps than normal computers for some tasks; because the rate of growth of quantum computers is so massive, its only a matter of time before they can do even those tasks better than normal computers.
It's also worth pointing out that not many algorithms have been found that work to quantum computers advantages, but it is almost inevitable that more will be found once we get closer to a working prototype.
In short, I don't know when quantum computers will appear in the 'mainstream', but when they do; they'll revolutionise everything completely.