Do we have an example of a real quantum computer doing some kind of a computation that is not easily accessible by the regular computer?
I keep hearing about "the promise" and "achieving quantum supremacy" (again!), but is there a real example of a quantum machine doing something useful in real life?
No, there are none; the closest we currently have are various special purpose and more or less hard-coded machines that demonstrate that scaling exists; various general-purpose machines operating on handfuls of qubits demonstrating the various gates; and various snake oil scams that may or may not have semi-respectable research divisions associated with them.
The Venn diagram of "useful" and "not possible on a classical computer" has demonstrations on both disjoint ends but is currently empty in the intersection. For now. I fully sympathize with the hype-fatigue though.
That's on the useful end but I don't think any QC has gone beyond being able to factor 14 or something in that neighborhood. Realistically we'd need a few thousand qubits to factor anything that's reasonable and current QCs have a dozen or so qubits that work.
The "factorization" done with quantum computers involved cherry picking special numbers so that a special "compiled" circuit (knowledge of the answer is required in order to do this) can be used instead of the full thing. That makes the semantics of the executed program "slightly" different.
> Do we have an example of a real quantum computer doing some kind of a computation that is not easily accessible by the regular computer?
Simulations of condensed matter simulations performed on QCs (google's OTOCs, quantinuum's HUbbard model) are not easily accessible by the regular computer. There are people working hard on simulating these results classically so it's quite likely they'll be simulated eventually. We're at point where classical computers are still in the race thanks to immense scale and algorithmic progress, but I think it won't be the case soon.
> something useful in real life?
usefulness is subjective. There are results that are potentially interesting to some people on Earth (as opposed to RCS).
No. It's as if there's a "No computing with this shit" theorem, enforced by nature alongside "No FTL communications," "No hidden variables," "No, you can't build a transporter, not yours," and "No cloning."
I keep hearing about "the promise" and "achieving quantum supremacy" (again!), but is there a real example of a quantum machine doing something useful in real life?