A brief history of quantum vs classical computational advantage
For researchers and policymakers, it provides a critical assessment of quantum advantage claims, highlighting that most are contested or incremental.
This review catalogs all experiments claiming quantum computational advantage, analyzing challenges and refutations, and discusses theoretical advantages in optimization and recommendation systems, concluding that quantum error correction is the key frontier for Shor's algorithm.
In this review article we summarize all experiments claiming quantum computational advantage to date. Our review highlights challenges, loopholes, and refutations appearing in subsequent work to provide a complete picture of the current statuses of these experiments. In addition, we also discuss theoretical computational advantage in example problems such as approximate optimization and recommendation systems. Finally, we review recent experiments in quantum error correction -- the biggest frontier to reach experimental quantum advantage in Shor's algorithm.