Technology

Yes, but, quantum TPM or TPU chips would allow for far more complex encryption. So you'd likely have a portiion of the SOC with a quantum bus or some other function.

However you're correct that it'd take a seachange in computing for a qbit based OS

Why are you isolating a single algorithm? There are tons of them that speed up various aspects of linear algebra and not just that single one, and many improvements to these algorithms since they were first introduced, there are a lot more in the literature than just in the popular consciousness.

The point is not that it will speed up every major calculation, but these are calculations that could be made use of, and there will likely even be more similar algorithms discovered if quantum computers are more commonplace. There is a whole branch of research called quantum machine learning that is centered solely around figuring out how to make use of these algorithms to provide performance benefits for machine learning algorithms.

If they would offer speed benefits, then why wouldn't you want to have the chip that offers the speed benefits in your phone? Of course, in practical terms, we likely will not have this due to the difficulty and expense of quantum chips, and the fact they currently have to be cooled below to near zero degrees Kelvin. But your argument suggests that if somehow consumers could have access to technology in their phone that would offer performance benefits to their software that they wouldn't want it.

That just makes no sense to me. The issue is not that quantum computers could not offer performance benefits in theory. The issue is more about whether or not the theory can be implemented in practical engineering terms, as well as a cost-to-performance ratio. The engineering would have to be good enough to both bring the price down and make the performance benefits high enough to make it worth it.

It is the same with GPUs. A GPU can only speed up certain problems, and it would thus be even more inefficient to try and force every calculation through the GPU. You have libraries that only call the GPU when it is needed for certain calculations. This ends up offering major performance benefits and if the price of the GPU is low enough and the performance benefits high enough to match what the consumers want, they will buy it. We also have separate AI chips now as well which are making their way into some phones. While there's no reason at the current moment to believe we will see quantum technology shrunk small and cheap enough to show up in consumer phones, if hypothetically that was the case, I don't see why consumers wouldn't want it.

I am sure clever software developers would figure out how to make use of them if they were available like that. They likely will not be available like that any time in the near future, if ever, but assuming they are, there would probably be a lot of interesting use cases for them that have not even been thought of yet. They will likely remain something largely used by businesses but in my view it will be mostly because of practical concerns. The benefits of them won't outweigh the cost anytime soon.