# Quantum-query complexity comparison ledger

Family 284: The optimal quartic separation between randomized and quantum queries. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Query-algorithm researchers can record the sharp quartic randomized-versus-quantum separation for total Boolean functions.

## Applicability and commercial boundary

Worst-case bit-query complexity permits unrestricted intervening computation and therefore does not establish end-to-end runtime, financial return or practical quantum advantage.

## Initial business decision

Research infrastructure. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Add query-model fields and total-cost exclusions to opportunity 020.

## Evidence scope

The catalog statement was individually reviewed. This record does not imply a manuscript proof review or formal-scope comparison. No independent Lean check was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Main source

[A Nearly Quartic Separation Between Randomized and Quantum Query Complexity](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Nearly-Quartic-Separation-Between-Randomized-and-Quantum-Query-Complexity-October-5-2026/quartic-query-separation.pdf).