You want a use case for mobile quantum computing power? Here:

One problem quantum computing presents is that its computing potential overrules all current encryption mechanisms right? If your beautiful centralised computing solution can easily decrypt any data stream encrypted by conventional means then you’ll probably need an equally advanced solution to encrypt your data.

Another: a mobile running a 20-year-in-the-future graphics/physics game engine to simulate an AR reality over 10G internet together with 40.000 other players using the 20 different cameras in your phone that observe x-rays throughout microwaves while streaming to your 4D headset.

I’m certain there are mathmaticians and IT scientists out there who can elaborate on why this is/isn’t a bs use case. My point is that if I can come up with a potential use case in seconds while I’m cooking diner, then it’s plain dumb to assume that TONS of people won’t come up with actual use cases in the coming 20 years.

There is something of a trend of a pendulum swinging between centralization and decentralization in computing.

Mainframes where you had to physically sit at and perform batch processing eventually had time-sharing capability added via remote terminals. Centralization came back when we got PCs, which then gave way to having data available on the internet. Our phones became computers, and then fast mobile data connections let us shift applications and processing into the cloud.

If it's physically possible to have a quantum computer at home, or in our pocket, we probably will. If I had to guess based on how we do things today, I'd say that those quantum processing capabilities will probably be used for co-processing for very specific applications. Maybe quantum cryptography? And anything more general, or requiring a large amount of qubits, will be available via the cloud.