This is the true key question: what are the most important algorithms that would be accelerated by quantum computing?
Some candidates:
- Shor's algorithm: this one will actually make humanity worse off, as we will be forced into post-quantum cryptography that will likely be less efficient than existing classical cryptography to implement
- quantum algorithm for linear systems of equations, and related application of systems of linear equations
- Grover's algorithm: speedup not exponential. Still useful for anything?
- Quantum Fourier transform: TODO is the speedup exponential or not?
- Deutsch: solves an useless problem
- NISQ algorithms
Do you have proper optimization or quantum chemistry algorithms that will make trillions?
Maybe there is some room for doubt because some applications might be way better in some implementations, but we should at least have a good general idea.
However, clear information on this really hard to come by, not sure why.
Whenever asked e.g. at: physics.stackexchange.com/questions/3390/can-anybody-provide-a-simple-example-of-a-quantum-computer-algorithm/3407 on Physics Stack Exchange people say the infinite mantra:
Lists:
- Quantum Algorithm Zoo: the leading list as of 2020
- quantum computing computational chemistry algorithms is the area that Ciro and many people are te most excited about is
- cstheory.stackexchange.com/questions/3888/np-intermediate-problems-with-efficient-quantum-solutions
- mathoverflow.net/questions/33597/are-there-any-known-quantum-algorithms-that-clearly-fall-outside-a-few-narrow-cla