(Note: my English might be insufficient at some points. Sorry if it's distracting.)
How QC solutions work in theory
A good analogy of how they work would be this seemingly unrelated video. We see salt particles on a limited flat surface, navigating themselves into a certain pattern when they "hear" a sound with a specific wavelength. (It's all about the small integer ratios of the wavelength and the plane size; much like steady Lissajous curves, or chords in music.) The point is, they move around until they reach a state where they "like to stay".
Quantum Computers, according to their believers (and to the best of my knowledge), work similarly. They are a network of qbits taking every possible state (at once!) but they only get stable in a certain constellation - the one that satisfies your criteria. Then you go read their final state, and it should be the answer itself, or one of the likely answers. It's as if you calculated all points of a curve with the salt-and-sound method. Classical computers would do this like a particle emulator where you'd have to calculate every grain of salt; with this sound wave thing, you get an instant answer because salt is "everywhere" at the beginning, just as qbit states.
And this is nice - in theory.
will might never work
The problem is, you can't communicate with quantum bits. I mean, not really. Physicists have a theory, merely a theory, that such thing as superposition even exists. It's not a thing, it's an attempt to explain something we don't know. It's a method of working with unsure data. It's like saying "until you solve this equation, x has all the possible values, and then it suddenly collapses and takes on only one". Sure, it's one way to look at things; but it's not reality itself, it's just a side effect of missing information. If you already know x and I don't, then only I will have this uncertainty, and x, in fact, has a very specific value all along.
The same is true for quantum entanglement. According to the mainstream theory, when you observe one of the pairs, you gain instant information of the other. This sounds like magic, but it's like a pair of gloves: if we put them in two bags, then we both take one of the bags (random) and travel to the opposite ends of the galaxy, you will still know that if you have the left one in yours, then the right one was in mine. No information travels thru spacetime, nothing happens, only we know something on both sides - as soon as we "make the glove function collapse", aka check the bag. Yes, they say there's a wave function that collapses when you observe an entity; but again, this is not how it is, it's how we imagine it might as well be. It all goes back to the Copenhagen Interpretation, with a lot of debate around it, and honestly I'll open a champagne when they finally admit there's a better explanation. Even Schrödinger insisted that the probability approach to the poor cat's wellbeing is just wrong; it was a disproval of an explanation attempt, he said "guys this must be false because it leads to a contradiction in this simple thought experiment, the cat is dead and alive which is impossible"; instead, they accepted the impossible. A crazy theory about something having two states at once.
Superposition is probably a misunderstanding. Quantum computers will probably fail to deliver anything reliable; also they're very-very specific to a problem, you have to rewire them each time you want to add different numbers together, and even then, it's a very unstable way. It's like calculating the ratio of two numbers by cutting a plane to the right size, put salt on it, and then turn up the music.
- Quantum computers do NOT work, and it's not known if they ever will;
- They only ever will if we were right about the cat (which is unlikely);
- Efforts and expenses are way beyond the point of "worth it";
- The most practical problem they will ever solve is like factoring numbers;
- They will advertise the hell out of them no matter what.