Agfdhyk

By my first impression, there are many-qubits computers out there and more to come, as to follow the press.

Now a closer look reveals that it's all about designing and building physical qubits.

Then, as it seems from further reading, you actually need quite many physical qubits (dozens or hundreds) to come close to a practically usable logical qubit.

So does it mean after all, nobody has yet built any single logical qubit?

Note. This question is meant to understand the state of the art as applyied to computing, not to blame it!

A logical qubit is a very fluid concept. You could use physical qubits as logical qubits. Or, you can encode multiple physical qubits as a single logical qubit. The more physical qubits you use, the better the resistance to noise. So, I would suggest that you question isn't exactly the right one to ask, and a better question is whether something useful can be done with existing quantum technology (in the direction of computation).

The long-term goal is to build quantum computers, which require logical operations to be performed with a suitable level of reliability (below the "fault-tolerant threshold"), that can be maintained for a long time. It's true that we're probably not quite there yet, even with a single logical qubit. I don't actually know how close current hardware is to achieving it. That doesn't mean that existing devices are entirely pointless.

There is a lot of research going on at the moment into "quantum supremacy", in other words, given the sort of noisy quantum devices of 50-100 qubits that are starting to appear, is there anything that we could do with them that is unequivocally better than anything we could do with a classical computer? The expectation is that we're somewhere around that threshold at the moment, but I'm not aware of anything that is definitive.