A brief history of quantum vs classical computational advantage

TL;DR

The paper surveys the landscape of claimed quantum versus classical computational advantage, detailing major experiments (RCS, GBS, QSim) and the subsequent challenges and refutations that have shaped the field. It analyzes both experimental progress and theoretical notions of advantage, including approximate optimization, dequantization, and quantum chemistry, emphasizing that apparent speedups can be mitigated by improved classical algorithms or hardware developments. It also highlights quantum error correction as the critical path toward scalable, fault-tolerant advantage for tasks like Shor’s algorithm, while acknowledging the substantial engineering hurdles ahead. Overall, the review presents a dynamic, evolving boundary between quantum and classical computation, where the status of advantage continually shifts with new techniques, data, and hardware capabilities.

Abstract

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.