For RSA 4096 10^7 qubits with 10^-4 error rate (order of magnitude).

You can do useful and valuable quantum chemistry calculations already with few 100s of qubits with that low error rates, while post-quantum algorithms are becoming more common everyday removing incentives to build crypto cracking quantum computers.

I think the quantum computing will advance fastest in directions that are not easy to use in cryptography.

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HappyPanacea 6 days ago | parent | next [-]

Which valuable quantum chemistry calculations you can do with few 100s of qubits with that low error rates?

	▲	nabla9 6 days ago \| parent [-]
		The general idea is that with N fault-tolerant qubits, you can find the ground-state energy of an electronic system with N spin orbitals. 100 spin orbitals is the practical upper limit of current computers, so when you get into several hundred qubits, you can start seeing gains. In some special problems hybrid methods start giving gains in 100 qubits or below. Gate count estimates for performing quantum chemistry on small quantum computers https://arxiv.org/pdf/1312.1695 A Perspective on Quantum Computing Applications in Quantum Chemistry using 25--100 Logical Qubits https://arxiv.org/pdf/2506.19337

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smj-edison 6 days ago | parent | prev [-]

Honestly, if all quantum computers manage to pull off is quantum chemistry, I feel like that'll be enough. It would be a massive boon to the field of material sciences at any rate, which underlies so much of current infrastructure.