Practical Quantum Advantage — Performance Beyond Classical Computation on Relevant Problems

The claim has not been satisfied. No quantum computer has demonstrated advantage on a problem that simultaneously meets both the performance threshold (faster than best classical methods) and the practical relevance threshold (problem has genuine scientific or commercial value at the demonstrated scale). The evidence base contains strong demonstrations of one component without the other — advantage on demonstration problems (INST-001, 002, 004) or near-advantage on relevant problems (INST-005) — but no instance yet satisfies both simultaneously. IBM's quantum utility claim (INST-003) comes closest to bridging the two, reporting results on a problem with some scientific relevance that classical simulation was disputed to match, but the classical-simulation contest remains unresolved. The pressure state is FRAGMENTING: the evidence is splitting along two separate trajectories — demonstration-problem advantage growing stronger (INST-004) and relevant-problem simulation approaching but not reaching classical intractability (INST-005) — without converging on a single instance that would resolve the claim (OQ-001).