AUTHOR=Au-Yeung Rhonda , Chancellor Nicholas , Halffmann Pascal TITLE=NP-hard but no longer hard to solve? Using quantum computing to tackle optimization problems JOURNAL=Frontiers in Quantum Science and Technology VOLUME=2 YEAR=2023 URL=https://www.frontiersin.org/journals/quantum-science-and-technology/articles/10.3389/frqst.2023.1128576 DOI=10.3389/frqst.2023.1128576 ISSN=2813-2181 ABSTRACT=

In the last decade, public and industrial research funding has moved quantum computing from the early promises of Shor’s algorithm through experiments to the era of noisy intermediate scale quantum devices (NISQ) for solving real-world problems. It is likely that quantum methods can efficiently solve certain (NP-) hard optimization problems where classical approaches fail. In our perspective, we examine the field of quantum optimization, that is, solving optimization problems using quantum computers. We provide an entry point to quantum optimization for researchers from each topic, optimization or quantum computing, by demonstrating advances and obstacles with a suitable use case. We give an overview on problem formulation, available algorithms, and benchmarking. Although we show a proof-of-concept rather than a full benchmark between classical and quantum methods, this gives an idea of the current quality and capabilities of quantum computers for optimization problems. All observations are incorporated in a discussion on some recent quantum optimization breakthroughs, current status, and future directions.