Quantum advantage (sometimes “quantum supremacy”) names a demonstration that some quantum device solved a specific, well-defined computational task faster, or using resources, than any known classical method could match — as distinct from quantum computing’s longer-term goal of outperforming classical computers on tasks people actually want solved. Early demonstrations relied on random circuit sampling, where a circuit is chosen to be classically hard to simulate but the output itself cannot be independently checked; more recent claims, including analog simulations on quantum annealers, instead compare a quantum device’s output directly against a specific classical benchmark’s accuracy and runtime.
Because a quantum-advantage claim is a comparison against “the best known classical method” rather than a proof of a hard theoretical limit, individual claims have a track record of narrowing as classical algorithms improve. A later classical result matching part of an original benchmark does not by itself mean the whole claim was wrong — especially when the classical method still fails to match the hardest regimes originally tested.
Related papers
- King et al., “Beyond-classical computation in quantum simulation”, Science 388(6743), 199–204 (2025) — the original claim, a D-Wave quantum annealer’s spin-glass simulation reported as beyond classical reach.
- Tindall, Mello, Fishman, Stoudenmire, and Sels, “Dynamics of disordered quantum systems with two- and three-dimensional tensor networks”, Science 392, 868 (2026) — a classical tensor-network method that matches part of that benchmark.
- King, Nocera, Rams, Dziarmaga, Raymond, Kaushal, Sandvik, Alvarez, Carrasquilla, Franz, and Amin, “Comment on: ‘Dynamics of disordered quantum systems with two- and three-dimensional tensor networks’” (2026) — the original authors’ response, arguing the hardest parts of their claim remain unmatched. Covered in 2026-w32.