Can someone please explain why STO-3G is considered to be a good basis set for quantum computing, while it does not help in classical computing? I would also be very grateful for any references to read about as I could not find the needed information.
The only reason why we are using STO-nG for quantum computing is because current quantum hardware have limited number of qubits. If we have an ideal quantum computer with many qubits, we wouldn't want to use STO-3G but rather a more sophisticated basis set.
Here are some examples of the qubit requirement to represent the electronic Hamiltonian of $H_2$, $LiH$ and $H_2O$ using both STO-3G or cc-pVDZ (correlation-consistent poralized valence only double zeta) basis set under Jordan-Wigner transformation.
As you can see, we don't have the quantum resources to actually solve the electronic structure problem outside of the minimal basis set (STO-ng) at the moment. We have limited number of qubits, and the qubits we have are noisy!
Many literature papers seem to indicate "Chemical accuracy" calculation on quantum computer using STO-3G, and this might be the confusion... because what they ought to say is "Chemical precision". They are obtaining result within 1 mHA comparing to the exact diagonalization of the electronic Hamiltonian under STO-3G basis set discretization. But the true result maybe way off if the molecular system is complicated.
So in conclusion, we only use STO-3G because of the restriction we have with current quantum hardware. Not because it is better.
It should be noted that the graph showing the required qubits above is not taking into different qubit reduction techniques like qubit tapering and etc. People have been and are working on different quantum resource reduction schemes ( for example: here or here and many more..) to get the number of qubits required to represent a particular problem down... so they can run this particular problem on current quantum hardware.