As a data scientist, I want to use the cutting edge algorithms of machine learning to build my models, I am interested in quantum machine learning, the recent research in QML is about variational algorithms and other algorithms for NISQ machines, my question is, will these algorithms work in fault-tolerant quantum computers or we must design new algorithms such as Shor, Groover and HHL algorithms?
To my best understanding, one the challenges in quantum computing right now lies on the quantum noise that affects the fidelity of the qubits to reliable execute calculations. Fault-tolerant quantum computings are going to be capable of correct logical qubits faster than the rate of errors that will arise on the computation.
To, address the question, I think NISQ based algorithms can still be useful in later-stage fault-tolerant quantum computers precisely because of the error-correcting capabilities.
Case in point: right now quantum simulation of molecules is really hot. As far as I know from reading papers, quantum chemistry problems represent opportunities to test quantum computing. Even with errors present on the computation, researchers have found that current NISQ-quantum hardware will still converge to classical known answers.
However, what if you find yourself with the following challenge: you would like to simulate the interaction of a pair of copper ions in a MOF to calculate the relaxation times as a way to compare with experimental findings using NMR techniques.This was a problem I was interested in for my MS thesis. Unfortunately, this right now, as best as I know from speaking with Dr. De Jong, is not feasible using a NISQ-based quantum computer.
However, in the future, quantum computers may be able to tackle such a problem.
So, to conclude, the algorithm will be useful. Perhaps it may no longer be suitable given change in the computing paradigm - from NISQ to fault-tolerant quantum computing. Perhaps new algorithms will be found on the fault-tolerant regime that can outperform current algorithms. But all in all, it's not the NISQ-based algorithm, but the error-correcting capabilities that are one of the issues at the moment.
I can only conclude that if error-correcting is perfected to the level required to reach that paradigm of computation, that current NISQ-based algorithms run on fault-tolerant quantum computers will outperform current runs on current hardware.
One of the issues, again, as I understand it, is the error-correcting capabilities we have today and their impact on current quantum computing.