Hybrid quantum-classical algorithms in the noisy intermediate-scale quantum era and beyond

TL;DR

This paper discusses the nature, history, and future of hybrid quantum-classical algorithms, emphasizing their importance in the NISQ era and beyond, and proposing a definition based on the role of classical components in computation.

Contribution

It offers a broad conceptual framework for understanding hybrid algorithms, including a new definition based on the role of classical components, and explores their evolution and future in quantum computing.

Findings

Hybrid algorithms are defined by the crucial role of classical components.

Hybrid algorithms are likely to persist beyond the NISQ era into fault-tolerant quantum computing.

Quantum processors will augment classical computing by performing specialized tasks.

Abstract

Hybrid quantum-classical algorithms are central to much of the current research in quantum computing, particularly when considering the noisy intermediate-scale quantum (NISQ) era, with a number of experimental demonstrations having already been performed. In this perspective, we discuss in a very broad sense what it means for an algorithm to be hybrid quantum-classical. We first explore this concept very directly, by building a definition based on previous work in abstraction/representation theory, arguing that what makes an algorithm hybrid is not directly how it is run (or how many classical resources it consumes), but whether classical components are crucial to an underlying model of the computation. We then take a broader view of this question, reviewing a number of hybrid algorithms and discussing what makes them hybrid, as well as the history of how they emerged, and considerations related to hardware. This leads into a natural discussion of what the future holds for these algorithms. To answer this question, we turn to the use of specialized processors in classical computing.The classical trend is not for new technology to completely replace the old, but to augment it. We argue that the evolution of quantum computing is unlikely to be different: hybrid algorithms are likely here to stay well past the NISQ era and even into full fault-tolerance, with the quantum processors augmenting the already powerful classical processors which exist by performing specialized tasks.