[EvgeniyZh]

I don't agree. I do a bit of QC in my PhD, but my advisor works specifically on error mitigation, and from what I see, we'll soon (maybe a couple of years) be there: we'll have state-of-the-art simulations on quantum computer. There will be classical simulations that will improve on a specific claim, but eventually they'll die out.

But even if it is not true, think how good can be QC without being good enough for quantum error correction. You're saying orders of magnitude improvements are needed to be able to do EC, but I'm sure useful and interesting things can be done with log(QV) of 100, only 5 times more than current record.

[deepburner]

You're talking in very vague terms here, what does """interesting""" mean?

Let me give you some numbers. Factorising RSA is order 10^6 logical qubits (and I'm being charitable here), simulating FoMoCo is around 10^7. The state of the art error correction is around (again, charitably) 10^3 physical qubits per logical qubit at the moment, that gives us 10^9-10^10 qubits necessary for the simplest quantum application. We're at order 100 right now.

Peter Shot thinks that error correction can go down to 100 physical-per-logical, that's an order of magnitude shaved off there, but the algorithm itself is pretty basic, i don't see it getting any better there. Simulation algorithms have much better odds in seeing improvements as I think the gates used there are rather non-standard and have avenues for better gate compilation techniques.

[EvgeniyZh]

Well, I was talking specifically simulations of quantum systems (physical and chemical). Interesting is indeed vague, what I meant systems that people study outside of attempt to create a hard-to-simulate (classically) quantum system. Say, 2D Hubbard model or some 2D topological insulator.

Optimization (VQE, QAOA and stuff like that) also is realizable on NISQ. I'm more sceptical about its usefulness but it is hard to say.

Shor's algorithms is definitely outside of NISQ, I don't think anyone serious about QC thinks otherwise. From there to "no applications for NISQ" is a far fetch.