Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 284-01. A Nearly Quartic Separation Between Randomized and Quantum Query Complexity
Manuscript map · lines 8085–8094
OpenAI@2026-10-07#rem:oai-p-284-01
Authors: OpenAI. Family 284.
Title: A Nearly Quartic Separation Between Randomized and Quantum Query Complexity.
Abstract: We construct total Boolean functions with a nearly quartic separation between bounded-error randomized and quantum query complexity. Writing these complexities as ${}mathrm R(f)$ and ${}mathrm Q(f)$, the examples rule out every universal bound ${}mathrm R(f)=O((1+{}mathrm Q(f)){}{}alpha)$ with α < 4. Thus the known quartic upper bound has the optimal exponent, disproving the conjectured cubic bound. Both complexities count worst-case bit queries with error at most 1/3 on every input.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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