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For example, if you had an 8-bit integer represented by a bunch of qbits in a superposition of states, it would have every possible value from 0-256 and could be computed with as though it were every possible value at once until it is observed, the probability wave collapses, and a finite value emerges. Is this not the case?

Not really, or at least it's not a good way of thinking about it. Imagine it more like rigging coin tosses: You don't have every single configuration at the same time, but rather you have a joint probability over all bits which get altered to produce certain useful distributions.
To get something out, you then make a measurement that returns the correct result with a certain probability (i.e. it's a probabilistic turing machine rather than a nondeterministic one).

This can be very useful since sampling from a distribution can sometimes be much nicer than actually solving a problem (e.g. you replace a solver with a simulator of the output).
In traditional computing this can also be done but that gives you the fundamental problem of sampling from very complex probability distributions which involves approximating usually intractable integrals.

However, there are also massive limitations to the type of things a quantum computer can model in this way since quantum theory is inherently linear (i.e. no climate modelling regardless of how often people claim they want to do it).
There's also the question of how many things exist where it is more efficient to build such a distribution and sample from it, rather than having a direct solver.
If you look at the classic quantum algorithms (e.g. https://en.wikipedia.org/wiki/Quantum_algorithm), you can see that there aren't really that many algorithms out there (this is of course not an exhaustive list but it gives a pretty good overview) where it makes sense to use quantum computing and pretty much all of them are asymptotically barely faster or the same speed as classical ones and most of them rely on the fact that the problem you are looking at is a black-box one.

Remember that one of the largest useful problems that was ever solved on a quantum computer up until now was factoring the number 21 with a specialised version of Shor's algorithm that only works for that number (since the full shor would need many orders of magnitude more qbits than exist on the entire planet).

There's also the problem of logical vs physical qbits: In computer science we like to work with "perfect" qbits that are mathematically ideal, i.e. are completely noise free. However, physical qbits are really fragile and attenuate to pretty much anything and everything, which adds a lot of noise into the system. This problem also gets worse the larger you scale your system.

The latter is a fundamental problem: the entire clue of quantum computers is that you can combine random states to "virtually" build a complex distribution before you sample from it. This can be much faster since the virtual model can look dependencies that are intractable to work with on a classical system, but that dependency monster also means that any noise in the system is going to negatively affect everything else as you scale up to more qbits.
That's why people expect real quantum computers to have many orders of magnitude more qbits than you would theoretically need.

It also means that you cannot trivially scale up a physical quantum algorithm: Physical grovers on a list with 10 entries might look very different than a physical grover with 11 entries.
This makes quantum computing a nonstarter for many problems where you cannot pay the time it takes to engineer a custom solution.
And even worse: you cannot even test whether your fancy new algorithm works in a simulator, since the stuff you are trying to simulate is specifically the intractable quantum noise (something which, ironically, a quantum computer is excellent at simulating).

In general you should be really careful when looking at quantum computing articles, since it's very easy to build some weird distribution that is basically impossible for a normal computer to work with, but that doesn't mean it's something practical e.g. just starting the quantum computer, "boop" one bit, then waiting for 3ns will give you a quantum noise distribution that is intractable to simulate with a computer (same thing is true if you don't do anything with a computer: there's literal research teams of top scientists whose job boils down to "what are quantum computers computing if we don't give them instructions").

Meanwhile, the progress of classical or e.g. hybrid analog computing is much faster than that of quantum computing, which means that the only people really deeply invested into quantum computing are the ones that cannot afford to miss, just in case there is in fact something:

• finance
• defence
• security
• ....

(typed this out yesterday before @ZickZack s excellent answer, but couldn't post it at the time due to maintenance...)

No, you've got it wrong. This is a fairly common missunderstanding which is perpetuated by a lot of coverage about the topic being sloppy.

You could argue that there is a grain of truth to the idea of processing multiple possibilities at once, but it's a bit more complicated than that and the way it's usually presented leads to people building a bad intuition of how it works. If you do get in to the nitty-gritty of Shors algorithm it feels to me at least a bit like a weird hack that shouldn't work at all or at least not be faster than the normal way to compute prime factors. It isn't a general speedup, just in certain cases where you can exploit quantum mechanics in clever ways.

Of the top of my head the SMBC comic about it is actually pretty good. This article makes basically the same points, but a bit more elaborated (note that it was written a while ago so the part about the current state of quantum computing is outdated). I noticed that Veritasum put out a YouTube video which I haven't watched, but he is in my experience good at explaining physics and math so I think that there's a good chance that it'll hold up. I remember liking this Minute Physics video about Shor's algorithm too, if you wanna get a better understanding of it.

I should clarify that I'm not a quantum phycisist, I've just done a couple of internet deep dives on the topic but I can't say that I fully understand quantum computing at all. I do think my understanding of it is better than the one in this article and others like it.

More about quantum computing

Quantum computing, a remarkable leap in technological advancement, holds the potential to redefine our computational capacities. Harnessing the strange yet fascinating laws of quantum physics, it could significantly outperform classical computers in solving certain types of problems.

Basics of Quantum Computing

Traditional computers operate based on bits, which can be in a state of either 0 or 1. Quantum computers, on the other hand, operate on quantum bits, known as qubits. Unlike traditional bits, a qubit can exist in both states simultaneously, thanks to a quantum principle called superposition.

Superposition increases the computing power of a quantum computer exponentially. For example, two qubits can exist in four states simultaneously (00, 01, 10, 11), three qubits in eight states, and so on. This allows quantum computers to process a massive number of possibilities at once.

Another key quantum principle quantum computers exploit is entanglement. Entangled qubits are deeply linked. Change the state of one qubit, and the state of its entangled partner will change instantaneously, no matter the distance. This feature allows quantum computers to process complex computations more efficiently.

Applications of Quantum Computers

The unusual characteristics of quantum computing make it ideal for solving complex problems that classical computers struggle with.

Cryptography is a notable area where quantum computing can make a significant difference. The capacity to factor large numbers quickly makes quantum computers a threat to current encryption systems but also opens the door for the development of more secure quantum encryption methods.

In the field of medicine, quantum computing could enable the modeling of complex molecular structures, speeding up drug discovery. Quantum simulations could offer insights into new materials and processes that might take years to discover through experimentation.

Challenges in Quantum Computing

Despite its promising potential, quantum computing is not without challenges. Quantum states are delicate, and maintaining them for a practical length of time—known as quantum coherence—is a significant hurdle. The slightest environmental interference can cause qubits to lose their state, a phenomenon known as decoherence.

Quantum error correction is another daunting challenge. Due to the fragility of qubits, errors are more likely to occur in quantum computations than classical ones. Developing efficient error correction methods that don’t require a prohibitive number of qubits remains a central focus in quantum computing research.

The Future of Quantum Computing

While quantum computing is still in its infancy, the rapid pace of innovation signals a promising future. Tech giants like IBM, Google, and Microsoft, as well as numerous startups, are making significant strides in quantum computing research.

In the coming years, we can expect quantum computers to continue growing in power and reliability. Quantum supremacy—a point where quantum computers surpass classical computers in computational capabilities—may be closer than we think.

Quantum computing represents a thrilling frontier, promising to reshape how we tackle complex problems. As research and development persist, we inch closer to unlocking the full potential of this revolutionary technology.