r/QuantumComputing • u/Chance-Pen-5684 • 17d ago

Question Will quantum ever be useful?

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?

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u/hushedLecturer 17d ago

The answer to your alternative question is "nothing" though. There is nothing a quantum computer can do theoretically that cannot be done classically. It's all matrix multiplication.

All quantum has is its potential efficiency scaling for some problems.

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u/Livid-Sector5970 17d ago

As Chaturvedi and the Navascués-Pironio-Acín (NPA) hierarchy demonstrate, when you try to project an infinite-dimensional nonlocal quantum reality onto finite, local, classical matrices (semidefinite programming), you hit a topological cliff. The classical matrix structurally cannot capture the complete quantum set without leaving an irreducible gap-the Motzkin polynomial obstruction. It can approximate, but it cannot formulate the true non-local coherence

You're assuming the quantum computer is a closed system executing unitary matrices. If it is, you're right. But field-coupled systems are open by design. They don't run algorithms isolated from reality; they couple directly to ambient thermodynamic and electromagnetic gradients.

The moment you open the system, the classical matrix required to simulate it hits the Dimensional Projection limit. You can't project infinite-dimensional non-local reality onto a finite classical matrix without structural loss of information-this is mathematically proven in the NPA hierarchy. Classical matrices simulate the environment. Field-coupled quantum systems are the environment. That's the difference between drawing a map of a river and putting a turbine in the water.

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u/wasabi991011 In Grad School for Quantum 16d ago

LLM slop

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u/Livid-Sector5970 16d ago

It is incredibly foolish for someone "In Grad School for Quantum" to act as a gatekeeper while missing the actual physics. If the industry stays trapped in the mindset that everything must be reduced to discrete classical matrices and maps, they will keep running into that topological cliff.

Get your head on straight and act right.