On: Why haven't quantum computers factored 21 yet?

[HappyPanacea]

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

[nabla9 → HappyPanacea]

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