A brief history of quantum vs classical computational advantage

TL;DR

This review summarizes experimental claims of quantum computational advantage, discusses challenges and refutations, explores theoretical advantages in specific problems, and reviews progress in quantum error correction crucial for future quantum advantage.

Contribution

It provides a comprehensive overview of the history, challenges, and recent developments in achieving and verifying quantum computational advantage.

Findings

Multiple experiments claiming quantum advantage are analyzed with identified challenges.

Refutations and loopholes have been addressed in subsequent work, refining the understanding of experimental claims.

Recent progress in quantum error correction is highlighted as key to future quantum advantage.

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.