Where are we heading with NISQ?

In 2017, John Preskill defined Noisy Intermediate Scale Quantum (NISQ) computers as an intermediate step on the road to large scale error corrected fault-tolerant quantum computers (FTQC). The NISQ regime corresponds to noisy qubit quantum computers with the potential to solve actual problems of some commercial value faster than conventional supercomputers, or consuming less energy. Over five years on, it is a good time to review the situation. While rapid progress is being made with quantum hardware and algorithms, and many recent experimental demonstrations, no one has yet successfully implemented a use case matching the original definition of the NISQ regime. This paper investigates the space, fidelity and time resources of various NISQ algorithms and highlights several contradictions between NISQ requirements and actual as well as future quantum hardware capabilities. It then covers various techniques which could help like qubit fidelities improvements, various breeds of quantum error mitigation methods, analog/digital hybridization, using specific qubit types like multimode photons as well as quantum annealers and analog quantum computers (aka quantum simulators or programmable Hamiltonian simulators) which seem closer to delivering useful applications although they have their own mid to longer-term scalability challenges. Given all the constraints of these various solutions, it seems possible to expect some practical use cases for NISQ systems, but with a very narrow window before various scaling issues show up. Turning to the future, a scenario can be envisioned where NISQ will not necessarily be an intermediate step on the road to FTQC. Instead, the two may develop along different paths, due to their different requirements. This leaves open a key question on the trade-offs that may be necessary to make between qubit scale and qubit fidelities in future quantum computers designs.