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Has quantum advantage been achieved?

Quantum computational advantage was claimed for the first time in 2019 and several experiments since then have reinforced and strengthened the claim. At the same time, a new generation of quantum computing devices with 100 logical qubits is being built. This raises two questions: Has quantum advantage actually been achieved? And what should our next milestones be for the upcoming 100-logical-qubit era? In this perspective, I argue that, in fact, quantum advantage has been achieved. The status today is analogous to Bell-inequality violations in the 1980s where some loopholes remain open, specifically, scalability and verifiability. I then outline three milestones for the 100-logical-qubit era aiming to close those loopholes: demonstrate fault-tolerant quantum advantage, perform efficiently verifiable advantage using random circuits with symmetries, and eventually demonstrate classically verifiable advantage with applications to certified randomness. These milestones are also natural stepping stones towards running algorithms with cryptographic applications.

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A brief history of quantum vs classical computational advantage

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.

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