What do you mean, how does it work? It’s complicated. The simple explanation is the one you just posted.
A ‘normal’ computer, like the one you are typing on, the one in your washing machine, the one in your car, the one the Met Office use, has a CPU that has large number of bytes of memory. It starts at a specific point in memory then each byte is an instruction to do something like add or comapre numbers, or jump to a different part of memory. This is called Von Neumann architecture and has been around forever and a day. So you write programs to work stuff out, you break mathematical problems down into steps like you would do with say long division or something. So much so that people think breaking down tasks into simple steps is synonymous with all software. This isn’t true for the kind of software in which I specialise, which leads to endless frustration when people give you their requirements.
But it’s not the only way to compute things. There used to be such things as analogue computers and all sorts of exotica. You could have a box of electronics where you put X volts into one terminal and the square root of X volts comes out of the other terminal. That’s a computer, cos it’s computing square roots, but it’s not going through a series of steps to calculate an answer like Windows Calculator does. It’s just set up so that an input is associated with an output in such a way that solves a given problem.
Quantum mechanics then. One rule of this is that observing amy system must change it, because you are interacting with it. Following on from that, until you DO observe a system, it’s impossible to tell what state it’s in – furthermore, it doesn’t matter, and even furthermore still, it can be considered to be in all states at the same time. This is what Schroedinger was getting at with the cat.
So a quantum computer contiains particles in a whole mess of states linked together in such a way that by interacting with its inputs its outputs can only exist in the state that represents the solution to the problem it’s been designed for. A bit like the analogue computer mentioned previously.
Now I don’t really know anything about current QC research, but that’s how it works generally afaik. I could be wrong of course.