If results from methods with higher electronic structure accuracy than DFT (MP2, couple cluster) can be made cheap enough, it would hugely disrupt industrial chemistry, medical experimentation, pharmaceuticals, the energy sector, etc.
Ground state and activation energy estimation for chemistry would be really useful. I know chemists are looking specifically at nitrogen fixation as one useful example.
Or as another example, I'm currently at a conference listening to a PhD student's research on biomolecular structure prediction (for protein design).
Energy levels and activation energies can be acquired much more simply from Fourier Transform - Ion Cyclotron Resonance - Mass Spectroscopy...
Its a device that makes and analyzes at the same time, check out this primer:
https://warwick.ac.uk/fac/sci/chemistry/research/oconnor/oco...
Factorization could have number theory implications I suppose. Using quantum effects to break cryptography wouldn't have any real long term advantages unless you aspired to be some sort of a supervillain.
> Using quantum effects to break cryptography wouldn't have any real long term advantages unless you aspired to be some sort of a supervillain.
It's of interest to governments, for national security reasons. Quantum computing is an arms race.
If you want O($10 billion per year) of funding, those numbers can only come from having $10 billion a year of impact balanced against your chance of success. The only application of QC worth $100+ billion is breaking cryptography.
PQC is as much a tool to reduce funding for QC as it is a tool against an actual eventual quantum computer.
All those other applications, no matter how neat, I feel are quite niche. Like, "simulate pairs of electrons in the Ising model". Cool. Is that a multi-billion dollars industry though?