Here's a bit of an ELI5 about quantum computers, and why this type of news are not nearly as much of a big deal as they appear.

To create quantum computers you need to be able to manipulate small particles like electrons, or ions. You need to be able to "freeze" them in a "superposition" state. If you think of a particle as a tiny magnetic needle, you need to be able to make the particle be in a "half North, half South" state, like Schroedinger's cat, which is half dead, half alive. What this means, is that you don't know if the needle points North or South (the usual terms in quantum computing are "spin up" and "spin down"), and nobody can know that; but you know that if you perform a measurement you will have exactly 50% chance to be North and 50% chance to be South. And by "manipulate", I mean, you can choose different such probabilities, for example 70% and 30%.

So far, so good, nothing too interesting happens.

But then, if you want quantum computation, you need to manipulate more than one particle. Let's say you want to manipulate 2 particles.

Now you can say, if I can freeze one particle, then I can freeze 2, what's the big deal. The big deal, is that the concept of freezing 2 particles involves "entanglement", or, as Einstein called it, "spooky action at a distance". For example, not only are you able to arrange then so that each has a probability to be, let's say 70% spin up and 30% spin down, but you can arrange them so that they always point in the same direction. If you measure one and you get up, then you know for sure that the other one will be up.

Now, this entanglement can lead to wonderful things, when it comes to computation. If you are smart and know how to entangle, let's say about 2000 particles, then you can factor large composite numbers or about 1000 bits length. And some people think this is a big deal (because of breaking passwords and stuff). Lots of people think it's not such a big deal after all, but let's not dwell on that.

Now, here's the problem. Entangling many particles is difficult. If you are able to entangle 5 particles, going to 6 is going to be difficult. But going from 6 to 7 is going to be about as difficult, and then from 7 to 8.

Here's [1] a link about IBM creating a quantum computer with 127 qubits (particles). They claim they'll achieve 1000 qubits sometime next year. That seems to contradict what I said in the paragraph above. Well, you can achieve more qubits if you relax what you call "entanglement", but then your algorithms will not perform as well, so it's not clear you can still achieve the exponential speedup needed to factor large numbers.

Anyway, back to the principles of quantum computation. The way you perform a computation is by first "freezing" or "entangling" the qubits, let's say you make them all fully entangled to point up with 50% probability. If you measure one, and you get up, you know all the others are up.

Now, here's the big deal: you can perform changes to this ensemble of qubits, while keeping them entangled. You can "rotate" them. And if your rotation is judiciously chosen, then when you perform the measurement, you'll get a 50% chance to get, let's say up, up, down, up, down, etc, or 11010... where this binary number gives you the answer to a problem you care about. Of course, you'll get a 50% chance to get a different number that's garbage, but you don't mind, because you can check your solution, and you can repeat the computation several times.

But the number of problems where such a smart rotation is possible is not that large. Many times you don't get an exponential speedup, but just a quadratic one.

The case with an exponential speedup is called quantum Fourier transform. If you can reduce a problem to the calculation of a quantum Fourier transform, then you are all set, you can achieve exponential speedup using quantum computers. The genius of Schor [2] was to show how to reduce the factoring problem to the quantum Fourier transform problem.

Unfortunately, not that many problems can be reduced to the quantum Fourier transform problem. So, assuming one day we'll have quantum computers with 1 billion qubits, if your problem cannot be reduced to the quantum Fourier transform problem, that fancy quantum computer will be quite useless for you.

[1] https://www.nature.com/articles/d41586-021-03476-5

[2] https://en.wikipedia.org/wiki/Shor%27s_algorithm