While scalable, fully error corrected quantum computing is years or even decades away, there is considerable interest in noisy intermediate-scale quantum computing (NISQ). In this paper, we introduce the ArsoNISQ framework that determines the tolerable error rate of a given quantum algorithm computation, i.e. quantum circuits, and the success probability of the computation given a success criterion and a NISQ computer. ArsoNISQ is based on simulations of quantum circuits subject to errors according to the Pauli error model.ArsoNISQ was evaluated on a set of quantum algorithms that can incur a quantum speedup or are otherwise relevant to NISQ computing. Despite optimistic expectations in recent literature, we did not observe quantum algorithms with intrinsic robustness, i.e. algorithms that tolerate one error on average, in this evaluation. The evaluation demonstrated, however, that the quantum circuit size sets an upper bound for its tolerable error rate and quantified the difference in tolerate error rates for quantum circuits of similar sizes. Thus, the framework can assist quantum algorithm developers in improving their implementation and selecting a suitable NISQ computing platform. Extrapolating the results into the quantum advantage regime suggests that the error rate of larger quantum computers must decrease substantially or active quantum error correction will need to be deployed for most of the evaluated algorithms.

First quantum computers very recently have demonstrated “quantum supremacy” or “quantum advantage Executing a computation that would have been impossible on a classical machine. Today's quantum computers follow the NISQ paradigm: They exhibit error rates that are much higher than in conventional electronics and have insufficient quantum resources to support powerful error correction protocols. This raises questions which relevant computations are within the reach of NISQ architectures. Several NISQ-era algorithms” are assumed to match the specifics of such computers; for instance, variational optimisers are based on intertwining relatively short quantum and classical computations, thus maximizing the chances of success. This paper will critically assess the promise and challenge of NISQ computing. What has this field achieved so far, what are we likely to achieve soon, where do we have to be skeptical and wait for the advent of larger-scale fully error-corrected architectures?

We provide a basic introduction of the core ideas and theory surrounding fault-tolerant quantum computation. Quantum fault-tolerance essentially refers to avoiding the uncontrollable cascade of errors caused by the interaction of quantum-bits. The presented concepts underlay the theoretical framework of large-scale quantum computation and are the driving force for many recent experimental efforts to construct small to medium sized arrays of controllable quantum bits. We examine the basic principles of redundant quantum encoding, required to protect quantum bits from errors generated from both imprecise control and environmental interactions. The novelty of this work consists in the presentation of fault-tolerance principles from a classical distributed computing perspective, as this enables a more straightforward introduction without sacrificing generality. The practicality of fault-tolerant quantum computing is analysed after introducing a metric of scalability and discussing the factors influencing it.

The realisation of large-scale quantum computing is no longer simply a hardware question. The rapid development of quantum technology has resulted in dozens of control and programming problems that should be directed towards the classical computer science and engineering community. One such problem is known as Pauli tracking. Methods for implementing quantum algorithms that are compatible with crucial error correction technology utilise extensive quantum teleportation protocols. These protocols are intrinsically probabilistic and result in correction operators that occur as byproducts of teleportation. These byproduct operators do not need to be corrected in the quantum hardware itself, but are tracked through the circuit and output results reinterpreted. This tracking is routinely ignored in quantum information as it is assumed that tracking algorithms will eventually be developed. In this work we help fill this gap and present an algorithm for tracking byproduct operators through a quantum computation.

Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction code, required to correct for inevitable hardware faults that will exist for a large scale quantum device. It is also a measurement based model of quantum computation, meaning that the quantum hardware is responsible only for the construction of a large, computationally universal quantum state. This quantum state is then strategically consumed, allowing for the realisation of a fully error corrected quantum algorithm. The number of physical qubits needed by the quantum hardware and the amount of time required to implement an algorithm is dictated by the manner in which this universal quantum state is consumed. In this paper we examine the problem of algorithmic optimisation in the topological lattice and introduce the required elements that will be needed when designing a classical software package to compile and implement a large scale algorithm on a topological quantum computer.