Quantum computing in the NISQ era and beyond
“Intermediate scale” refers to computers with between 50 and a few hundred qubits. The 50 qubit milestone is significant because that takes us beyond what we can simulate by brute force using the most powerful existing supercomputers. “Noisy” emphasises that we’ll have imperfect control over those qubits. Because of the noise, we expect a limit of about 1000 gates in a circuit – i.e., 1000 fundamental two-qubit operations. Executing a single gate is about 1000 times slower on an ion trap quantum processor than on a superconducting circuit.
Regarding the near future potential of quantum computers.
For a look at the past, Shor’s Algorithm: https://blog.acolyer.org/2018/02/02/polynomial-time-algorithms-for-prime-factorization-and-discrete-logarithms-on-a-quantum-computer/