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.

  • Good point about quantum supremacy! Thank you – J. Doe Nov 8 at 9:02
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    "The expectation is that we're somewhere around that threshold at the moment" are you sure about this? I would say that the threshold is at ~50 perfect qubits, I am not sure the 50-100 ultra-noisy qubits we have now can be used to anything serious (it is my opinion, you can disagree of course). – Nelimee Nov 8 at 9:20
  • "are you sure about this?" @Nelimee no he is not. (and he clearly says so) That statement is wrapped in like 5 layers of conditionals and uncertainty, as well as referencing very vague "sources" clarifying that he (as well as the rest of the world in his opinion) is absolutely not sure – Hobbamok Nov 8 at 10:55
  • @Nelimee No - I'm not up to date with the literature on supremacy, or with the details of what current hardware is precisely capable of. I'm really talking there about a couple of comments that people have made in seminars that I've been to in the past year or so, people who should know better than me (but it doesn't mean that they do, and I certainly don't have a referenceable source) – DaftWullie Nov 8 at 11:36
  • I might be out of date but iirc the Martinis group was the closest to getting fault-tolerant enough qubits and Scott Aaronson had some proposal for how to prove quantum supremacy that could be the best bet currently. – JollyJoker Nov 8 at 12:10

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