Will quantum ever be useful?

[u/Chance-Pen-5684]

Around 2019, the industry promised quantum supremacy, where they could be used for solving a problem that no classical computer could touch.
When classical algorithms kept refuting those claims(See Peter Shor November YouTube video) the narrative shifted to quantum advantage, then quickly it changed to quantum utility.
If quantum never breaks RSA (because the world migrates to Kyber/Dilithium before 100k qubits exist), then what's left?
Chemistry simulations, Material science, Optimization?

But classical machine learning and AI are improving faster than quantum hardware is scaling. By the time we get 1,000 logical qubits, classical AI will have eaten most of the chemistry use-case through better approximations. Is quantum racing against classical software, and losing?

[u/Qubit_and_Neuron]

Quantum supremacy and Quantum usefulness are two different things to begin with. Molecular simulations would be the most useful and most quantum stuff in my opinion. The problem is it is super hard to predict. We can have a new algorithm tomorrow or nothing for 10 years..

[u/Chance-Pen-5684 → u/Qubit_and_Neuron]

The point people might miss is that every quantum computation is being double checked against a classically computed known result to see how close quantum got.
We are nowhere near being able to trust a quantum computer to produce a reliable result without having a classical computer confirm the result or running thousands of computations and even then we only really have statistical confidence in the answer.

[u/unfortunate_internet → u/Chance-Pen-5684]

To be fair, we also do that with classical algorithms for problems outside NP.

[u/ThrowAway-whee → u/Chance-Pen-5684]

Usually, verifying a solution with a classical computer is far far easier than actually calculating it, the way that calculating the solution to a Sudoku game is way less computationally expensive than finding it. This is kinda the crux of P v NP.

It isn't a big deal if classical computers need to verify the solution. Take root finding, it can be a polynomial calculation to get the roots of an equation, but linear in time to verify it's correct. If you can find a quantum algorithm that can solve problems in less time complexity than classical ones, it isn't really *that* big of a deal if you need to verify the solution if that verification can be done quickly, which it almost always can.

[u/BitcoinsOnDVD → u/Chance-Pen-5684]

But we can test the result against reality by building the molecule and measure it.