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Markets / Computer science / Quantum computation

Quantum sampling can exceed classical computing.

Can a quantum computer efficiently generate a pattern of random results that no classical computer can match efficiently? This is a mathematical claim, not a speed benchmark.

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Weekly AI estimate

52% This week · Nov 10, 2026 09:25 PM EST

The average of three models reading the same evidence. It is an estimate, not proof the hypothesis holds, and it does not set the pool price.

Range
2–95%
Verdict
Undecided

The panel's confident binary this round Undecided the models did not all agree

0% 25% 50% 75% 100%
OpenAI 95% Anthropic 2% xAI 58% Average 52%
Market definition · YES, NO and evidence rules

This is the frozen contract wording. Read the YES and NO tests, the evidence requirements and the undecided cases before taking a position.

Canonical title

Efficient quantum sampling exceeds efficient classical sampling.

Exact hypothesis · technical wording

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.

Each round reads the evidence that was public at a stated cutoff. Later evidence goes into a later round; the market itself has no expiry date.

How the evidence cutoff is fixed

A round only counts evidence published before its own cutoff time, and the round's number is that timestamp. So a round cannot borrow a later cutoff, and an earlier round's judgment cannot be reused for a later one. The hypothesis wording, the resolution criteria and the methodology identifier were hashed into the market account at creation, which is what stops any of them being edited afterwards.

Resolution criteria

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.

The definition does not change when an AI estimate changes. Read the listing policy and this market's settlement status.

How each model argued

Three models read the same evidence and did not fully agree. Their average is 0.52.

This round ran under methodology panel-v9. Short excerpts are below; the round 5 page keeps the full answers, sources and raw responses. The current methodology and example requests do not reconstruct this historical round's exact request.

OpenAI UNDECIDED 0.95

openai/gpt-6.1-sol

I read the hypothesis as an unrelativized separation under the specified uniform approximation definition. Conditional sampling-hardness results strongly favor separation, but the checked primary reference requires unproved conjectures and…

Would change this view: A verified unconditional proof of equality would reverse my estimate; a verified separation proof matching the uniform approximation definition would establish YES.

Full explanation from OpenAI→
Anthropic UNDECIDED 0.02

anthropic/claude-sonnet-5.5

I found no unconditional ZFC proof that SampBQP differs from SampBPP, and no proof that they are equal. An unconditional separation would likely imply unresolved results such as P≠PSPACE. The known results rely on assumptions: PH…

Full explanation from Anthropic→
xAI UNDECIDED 0.58

x-ai/grok-4.7

No unconditional ZFC proof separates or equates SampBQP and SampBPP under the stated uniform total-variation definition. Aaronson–Arkhipov hardness is conditional on polynomial-hierarchy or average-case conjectures, which the criterion…

Would change this view: A peer-reviewed unconditional ZFC proof equating or separating these classes for every uniform sampler.

Full explanation from xAI→

What moved the number

—
Oct 16

This is a new contract, not a migrated position or a continuation of old forecast history. The initial 0.50 is an initialization convention, not an AI forecast or an assessed scientific probability. Reference links are background sources,…

Nov 10
0.49 0.52 +2.7

OpenAI estimated 0.95. I read the hypothesis as an unrelativized separation under the specified uniform approximation definition. Conditional sampling-hardness results strongly favor separation, but the checked primary reference requires……

This round's saved score, answers and sources →
Nov 9
0.49 0.49 0.0 no model output

Live panel did not return all three estimates (OpenAI, Anthropic, xAI failed or gave an unusable answer). A round is only live when all three are valid, so this round is a placeholder at the previous score rather than an average of two.

This round's saved score, answers and sources →
Oct 19

OpenAI estimated 0.85. I interpret the hypothesis as an unrelativized separation under the stated uniform, total-variation approximation definition. Aaronson–Arkhipov provides substantial but conditional support: approximate-sampling…

This round's saved score, answers and sources →
—
Oct 19

AI estimate scheduled: an independent three-model panel reads the published definition and evidence every week. New positions are still closed for this market, so the estimate is here to read, not to trade against.

The evidence packet · 4 entries

What the panel was shown when this round ran. A row with no source link is a description only, and the panel is told so.

Aaronson and Arkhipov: The Computational Complexity of Linear Optics

Context

Primary theory paper distinguishing exact sampling and conditional approximate-sampling hardness.

Source link

Required positive observation

Supporting

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.

Description only · no source link recorded

Required contrary observation

Contrary

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.

Description only · no source link recorded

Eligibility and unresolved outcomes

Method

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.

Description only · no source link recorded

Past estimates

Every weekly estimate, newest first
DateEstimateRange
Nov 10, 2026 09:25 PM EST 52% 2–95%
Nov 09, 2026 09:33 AM EST 49% no live reading
Nov 02, 2026 09:33 AM EST 49% no live reading
Oct 26, 2026 10:33 AM EDT 49% no live reading
Oct 19, 2026 07:06 PM EDT 49% 2–85%

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