Efficient quantum sampling exceeds efficient classical sampling.

SampBQP differs from SampBPP for uniform sampling problems: the input includes unary 1/epsilon; sampling must be within total-variation distance epsilon of the target distribution in runtime polynomial in input length and 1/epsilon. Quantum algorithms use a fixed universal finite gate set; classical algorithms are randomized Turing machines. Nonuniform advice and postselection are excluded.

YES: An unconditional ZFC proof of the stated separation, with a quantum-samplable family and a lower bound against every uniform classical sampler under the same approximation definition. NO: An unconditional ZFC proof of equality of the stated sampling classes. A classical algorithm for one candidate family does not establish equality. A reduction relying on a conjectured noncollapse of the polynomial hierarchy is conditional and leaves this market UNDECIDED. Reference sources: Aaronson and Arkhipov: The Computational Complexity of Linear Optics (https://theoryofcomputing.org/articles/v009a004/). Evidence policy: use public primary research with methods and uncertainty, plus the named reference sources below. A preprint can inform the estimate but cannot alone meet a terminal criterion; require a peer-reviewed primary result and an independent reproduction using non-overlapping observations or independently prepared samples, unless this is a mathematical proof or the specific criterion instead requires independently implemented calculations. Report data provenance, exclusions, calibration, statistical model and systematic uncertainty. Independence means different data acquisition, not two papers reanalysing the same sample. For a quantitative terminal test, both independent results must meet the stated threshold; disagreement or an interval crossing the boundary means UNDECIDED. Use the final corrected version public at the signed round's evidence cutoff (UTC); exclude later evidence until a later eligible round. Every report in a terminal round must use the same cutoff, covered by the verified signed context and enforced by the configured terminal protocol; a different cutoff requires a new eligible round, never reinterpretation of a signed report or mutation of an immutable binding. This market has no calendar expiry. Retracted findings cannot supply a terminal result. If a named source disappears, use its DOI/publisher or an archived identical version, then an equivalent primary publication applying these unchanged definitions; if none is accessible, remain UNDECIDED, never substitute a different test. Missing data, failed replication, a null search outside the specified domain, or an untested alternative is not automatically NO. These are instructions for evidence assessment, not an automatic truth oracle: scientific interpretation and systematic-error judgment remain. Settlement follows the configured platform mode: terminal mode requires one valid round with all three frozen models returning the same explicit YES or NO and criterion_met=true; any UNDECIDED, failure or disagreement leaves it unresolved. Legacy proposal/challenge mode requires its recorded review process. Model agreement does not prove scientific truth. Invalidity is not NO and this text does not authorize a refund or cancellation: only a cancellation rule disclosed before exposure, if the configured contract supports it, can apply. Otherwise pause new entries and preserve holders' existing rights. Never reinterpret terms after listing.