A brief history of quantum vs classical computational advantage

Q: What does this research mean for the field?

Current claims of quantum computational advantage face significant challenges and refutations, and achieving definitive experimental advantage relies heavily on advancing quantum error correction. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

Ryan LaRose

doi:10.22331/q-2026-09-01-2198

September 1, 2026QuantumOpen Access

A brief history of quantum vs classical computational advantage

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Key Points

Synthesize and critically assess all experimental claims of quantum computational advantage alongside classical counterarguments and developments in error correction.
Reviewed historical and current literature detailing experimental claims of quantum computational advantage.
Surveyed theoretical advantage analyses across application areas including recommendation systems and approximate optimization.
Evaluated experimental progress in quantum error correction platforms relevant to executing Shor's algorithm.
Identified significant technical challenges, loopholes, and classical algorithmic improvements that refute or diminish several purported quantum advantage milestones.
Found that theoretical claims of computational advantage in approximate optimization and recommendation systems face competitive classical alternatives.
Determined that implementing fault-tolerant quantum error correction remains the primary unresolved requirement for achieving undeniable quantum advantage.

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Implication

Review uncovers persistent classical refutations against experimental claims in quantum processors, highlighting error correction as essential for definitive 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.

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Ryan LaRose (2026) studied this question.

synapsesocial.com/papers/6a993474636c6408cfa7c2b1 https://doi.org/10.22331/q-2026-09-01-2198

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A brief history of quantum vs classical computational advantage

Key Points

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A brief history of quantum vs classical computational advantage

Key Points

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