Abstract
Current quantum computing research is divided into two eras: near-term intermediate scaling quantum (NISQ) and fault-tolerant quantum computing (FTQC). There is a significant gap in these both in terms of hardware and algorithms. An important question is “how to transition from NISQ to FTQC”? Some research looks at an intermediate third era of quantum computing, sometimes referred to as “early” fault-tolerant quantum computing (EFTQC). The idea is to establish a trade-off between hardware and algorithmic parameters such that we have limited size circuits, albeit large enough to allow some amount of error-correction at the cost of more number of samples and increased run-time. This also requires adjustment to algorithms for various tasks. One way to do this is to allow the algorithm to tolerate some level of noise in the input. These algorithms are called “robust” quantum algorithms. In this chapter, we will understand what EFTQC means and how we can distinguish between the three eras of quantum computing. Furthermore, we will look at the ideas behind algorithms suitable for EFTQC devices. Lastly, we will look at two examples of robust quantum algorithms for the task of quantum phase estimation.